• BEACH EROSION SOARD

OFFICE OF THE CH IEF OF ENGINEERS

EQUILIBRIUM CHARACTERISTICS OF SAND BEACHES

IN THE OFFSHORE ZONE

TECHNICAL MEMORAN DUM NO. '26

!!RATA '& ""-' 1

8uc:b l~loa 8 .. = ':'ecMkal ~ .. JOIo. U,

.... U, JIQ . U) !'tId':

allould f.-d,

... ! [ .... r • ", .! ['In'

_ I -.r -,. -. IU (. - 't',J

a1n (' • ''')J "" If, 'J.c. 4 nld.;

,... 19 , Iq . ()()

A IId.1 11(,) •

•

r • [lU , L

III" 26 , Hilt n A.d., thould Alld l

.... .... ell .... "'Ur o ( Mdblllnt du-t,r o( Mdblll!!t

Jutt In .... (111 Cu t) Jlltt ill . . ..

he- 26 , HfIt a fn. bott_ !'tlcUl .... d ..... fllr of Md&.nt ill COfc: U .Ut1ftc •• ••

abould A ad l ,0' CliMetel" of "dl.ut Cia f .. t ) ia _lUatlr!t

h .. 61 , l.J..boI 14 rea6.1

Ibould nadl .... .... pll'Uc:llI .m

PIIrtlc:1e .1M In .taUC: (La ruu

.... 111 .tack

h .. 61, 1t. 1$ roadll

mould ."ad • .... tbt .1. ... ... .... 111 oKUUt 1llt .... ... . ( lo , .. t ) in OIIc:Ult t 1ll,

.... 62, l.J..boI 11 (I'M bon_

". ... d.1 .... _ell) ....

Ibould AadZ .... -.11) ••• •

62. 11M , 'I'M bott_ ...ad., ••••• !zed

~1d .... ,:11 .... . l2:e • .... ....

. ...

.. ..

EOUILIBRIUM CHARACTERISTICS OF SAND BEACHES

IN THE OFFSHORE ZONE

TECHN ICAL MEMORANDUM NO. 116 BEACH EROSION BOARD CORPS OF ENGINEERS

JULY 1961

The .0~_1Il of belch Uo4' ~ ". .... IcH/III ,. lbe 'i.a&I~ .. 51 boporUnt r.ct~ in 'IIor.U ... eballJ'l'" The "aetion o f tbe bead! to 1M c1ay-IC>-day variation. in ,"ve Ie Ii ... ' I , h_ver. ratlM!r eooopli­e.teo1 Ind. ..,r, f~ I1te~U hav. _<10 Md_ fa ulll<l .. tbe_tleJIll, the u.teuuion btt.IO budl .... !Id. &1111 ........

Thi. ~orandu. pr ... nla the result. of I laboratory study to e.tablish Iha equillbrlu. Itlll of • beleh undlr Ittaet fro. a liveo wave trlin . A ca.part.t on of these laboratory re.ultl .;th reaultl whidl wou1.d be l><pee led h_ tbeorr alone it dlo COfIhined ill the __ rand.... It il belle ... d IIlloI 1M defblltlon of the equiUbrlua n lallons au nece ... r, 10 ",In!.ft,.n urld""ulldinl of Ihe lIOn: COllJl lk.ted nUutl1 pho:n_na .hb hs conlfloua l .. ulation io waft patlern lad bueb profl.1.1.

'Ibll upotl .... prepare<:! at I~ Hrdr odyna.(u Laboratory at ,",nuchuselts Innltut<l of T.chnoiocy ill. punuln" of eontnet 0A-. 9-0"-eng-U .. illI the lleaeh II r o. lon Baird which provWn In part for t be 'Iud, of .ortln, 'nd onshore-offlhore lOY~nt of belch .lterUI. by ahln"", .... tel .... ve • . Tllia eonluet ..... uDder the gln_ enl aupanislon at 111<1 •• "".reh Diviaton of the BUCh I> rodoa Board. Tb<l luthor. of fhll r<lporl, P. S. e .,I.son, S. Gl.nne , Ind. J. A. Drlcup Ir<l aetber. o ( Ihe It. ff o f M •••• cbutett. tn.titute of Tecb­nolol1 . The itfvellt,:llIoo .... ean I."" oat uDder Ihill d It,,eti.na of A. T. I ppen, ProhuCK of H,.dnuliu, and lb. 'upo!f"'iliOll of p. S. IaClnon , AUiatln! 'roh •• or of H)'dflulle IDlilte<!rl.ol. TIM! "IP"ri­_nlat wor t on equilibri_ profUe. Ind sl"", .oula, ..... pClrfor.d, for the lOAf .,.rt, bp B. Glenna Ind. J. A. Dncup, nspeethel,.. k eaeuch AuiUuu H the lI,.drod,.... ... ea Laborator,..

vi .... &nd eOlle lu'{"n' .1Ivr.'ted in tbl. repol't .r. not neeel­Nr U, t hole of 111<1 Bueh lra.lon Boa rd.

""iI r.poet it publllhed • .odU uthorlty of PubUc Law 166 , ~th COGer •••• IpprOYWd Jul1 31, 19.$ .

TAaLl Of' CXlItl1JITS

!!1<

T.LI OP a:JImtJftS - - - - - 1

un OP I'~J All) TABUS - - lU

U$T 01' )t(I1'ATJDI'IS - - - - - • " .... "" - - 1

1 • """""''''1'''' - - - - • "- <re: .. ul SUt_, .( 'hi! ... obt- - - • ' . Scopt! o( , .

IllY .. ' ''.' loa • ". uv ..... I'kIIY IOUS 10., - ,

A. lqullibl'l_ a .. elI hotU •• - , •• Sed_fit Sortu., - - ,

111 . nl8:lUrrlCAt. tllVllOfMlltrn' - - - - 10

A. lquUlbrlg lIuchu - - 10

1. lI.c ~lround - - - - 10 •• tnclplf=lI t Motlc ... CrU ... tClOl " '. '.UbH.lhld MOlI_ Crltul_ - " •• kd.t.flt "'lu.. - - - " ... UP. DIEJrr AI.. IqUI PMUfT - ..

A. Va," ~o' . 1Id; Gao .... uter - " ' . V.," JIk.""'_1I1 llqulp. .. , - - - " C. ,.. Laborttor, 1I • • cft .~ Stnd - "

1. Iqulli~lu. I •• cft Prof lle.l " •• Sedt..IU Sor tu., bpar lJoe nU - - "

- - - - -

I. Sedbent So~t lna Iroc~ur.. _

A. RqulUbrlUll Beach Profile f:lxpe ~ u..n ti.

1 . Phy.lcsl Oe-.: ~ Iptlon of Rxpe rtn...ntsl Tel." 2. Theon I tea 1 leach p ~o r Uea l . Dl acuulan of Indh ldual Tests " , eo.pa~i.O<I of 8speru.enUI D .. t.

II , 5edlMnt So~ tlJlc Ilxpoe: ~ lMl\tl

1. !beont lesl SOrlJ.nc 2, Esper_ntat Sor lu.,

Vir, S~Y' NCn CDlCLU51011S __

VI IT . II!COCMEHDATH»G AlA ~\TTUl!I 51\1!lY'

"

---

-

-

-

!!.e

" " 32

" " " " " ., .. .. " 61

" " ..

LIST or nulJHES

Figure

1 Oe!"init.ion Sket.ch of aeal:.h Zonea

2 . NoUt.1on Oe!"1n1 t1on Sket.eb

3. !'oree De.f1n1t1on Sketch ., f 2(d)vs.<I r" r"

Incipient Motion Prott'le Furlction.

.!!e , 9

10

18

5 . ElIUlblilhed. Motion Profile Function, fl (<I ) vs. <I 24 r" t ,

6 . Ofhhore Bounduy Conditions fo r TheoretJ.coll 25 F.quillbrlWII Prorues b,. the Establhhed Hot.ion Crit.I1tlOl'l

7. Photograph of Wave Gsae and Cerr 11o€e 29

e. Sanborn 05~111orraph Trace ~

9 . Schell\atic Oiagr4l!\ of Beachell JO

10. Sieve Analysis of QttlDla Sane! JO

11. Phot.ogMlph of '''aves OYer Beach )6

12. Photograph of Typical Beach Configuration at Equi.librlWII J6

13. Chronological Variat.ion 1n R.nftCt i on Coeffic1 .mta )8

lJ.,

", 16,

17,

18 ,

Teat No. 1. Sea<:h ProfUes

Test No, '. Beach Prof Ues

Test Mo . J. Beach PTo!llu

Tut. No . '. Beach Profiles

Matched Exper1aental ll8ach ProfUes

Lo ., ., " La

19, 'nIflO'l'etical Sortinl t or I ncipient She Larger than tba SO Equilibrium S1~e at a 01ven Beach Position

20 . Theoretical Sort.1ng t or Incipient Siu !:bailer than the Equillbrilllll Siu a t a Given Beach Polition

'"

21. Coapartam of F1.n.Il SU. ,,"qu.11q tn.Lr1b\LtilB1 .,it.b 53 lndphnt (Di) and t.qv1libr1wo. (D.) 51 ... ror fen No. 6

22. Cao!p.rt.oo or F1.n.Il Sh. ,,"quenC)' D:1nrlbu.t.ion I/Ub Inc.lp1IJ1l' (Di) lind EquU1brt~ (D.) Si ... for T .. t 110. 1

23 . c.,.arison ot J'1nal S1.I.. 1T«juenq D:1.t.ribltUon wit.h .5.5 Incipient (D1) and IquU.1brtUII (DJ Sh .. Cor Tut No. a

24. Coapariaon or "HI! D111111.,,-r and Sort1nc Ccett1e1ent..l 1/1th 56 8ef,eh Position

2.5. Co!np&r1&on o! !nithJ. and. J'1.n&l She PrI!lq\lIlOC)' Dinr1lrDtiDn 5, ot fotal SandS~ ••

I SUMllary of Oat. Cor Equilibr1\111l ProtU. !:xJ,lerilllmti JJ

!l l'Te41cUon of Char.ot ... ot the t.qullibriua Beach P'rotU. 1.6 in !.h. atlahD..., Zone

I.

LIS! at NOTATlONS

o • wava tmpl1tude, ca . cr Ct,

~ , B.E,P ,Q .. coetricianta .. .ociatad With kine..tic wava p~art1aa ., lip e<li!1ed •

"1,"2

B:I., 8;!, 8 )

C

D

Do

D1

• coefticient. ... odated with waYe and und par ... etera u apec1tled

• ooettlc:iant. UIIociat&d Yit.b. wue and urul par_tu ...

• -='" val'e cala.rltT , Ct./ .. c,

coatticiant. "lOCia~ with V'l'a and sand sp&lIiIlad

.. co.ctiehnt oC l1It

... ~t part1cl, d1.ater, _., Ct., or hlc:bes .. IIp,dried

.. .""..,t. di_ter .. datandlled fro. "aquUllori_" IIrltarion. ft . , _ • • or inches • .., ~1ll.ad

.. aad1aent d.hrultllT " datar.tnocl rro. "1ncipiant.ft

e.r1te:rlOl1. ft., _ . , or ineb ..... apee1!hd

D.S. • ,ortal coaCrie1ent

d

•

r

- r

"

.. ,till v,t.tIT d.pth or c:oordinat.fl pe%'J)eMieu1ar t.o S.W.L. , ft. 01' 1lII •

.. bua of natural 10saritbJoa, 2.n8 .. . or su.bacript r.farr1ni to "flqUUibr1\1111" crit.r1on, .., lIpaciIied

.. coat'Uciant .. ,olli,ted 1dth Idnllllat!c: loIava proparLiaa

.. aubac:.r1pt. -C- ,..t8'tT1.n& t o arftoctba kineluU" nuid quantJ.t)' or to ph~·d"aJ propartT of fl.u1d

.. t.o denote a function .. lIpac1f1ad

.. n1l1d tor,,' on .. d1lllent particle, lbs.

•

'a I

'1.12

•

J

I

• ,

., p

q

• , •

• cr·rit.at.1~ tOTeS (111 a..u.~t. part,lell, lb ••

• V,Yi tat1.ontl conat.ant., 32 .2 r ... j aec."l

• to lIanotAI & t\u!.etion •• ~1!1.c

• wa .... bd,ht, cren. to t.rouih. _ . • ft.., OJ' ""'OM U

specified

• IIIIblcrtpt.· t" r e!err1..n& to lnddant. lin, Of IIIIbacrlpt. r.ren1.J\c to itlcipient. ertt..rian u eped.N.ed

• eoe!t1c1ent. • .,oelat..c viOl ", ..... and land p&nl!l.t.er~ u !rpee1tted

• coe!'1'1clant. ulIOC1.ated vi th .. ava and .tnd par •• t.are •• ~1C1t1e4

• ditferenca in onshore an" offshore _ent. on pill'Ucle Ill. reat., ft. lb ••

• coefticient. at paro.!'" ot ~oY1n8 part.icle.

• sub.r:rtp~ ·0" nterrtnc ,1th'l" to kin._tic cord!UonIJ in r lgion ot potential Oow or t.o dnp v_I.e.,.. ", ••• a_at.ry.

• ~c:ent.ll.

• two-c11.Ittndonal .ol~.t.r1c rat.a oJ now or ."I1_nt., ft.? Inc •

• •

•

•

non-d.1Nnalon&l l0l.ul!lltl"1C r.~. or nOlI or eed:blent., ... .,. ( .. I 'i'!-. Sllbcr1i!l "r r eIerri na to rille<:t.d wave Reynol" ~bil1' , baal'd on instantaneous rd.tive nu1d­led1.ment pVtlcl. velocity

apec1tic ,nrity or coord.1.nat.a alCllloI .. lid bot.w.

B.W.L.

, T

" U, U' o

",

v

,

,

'" (alpha)

'" , f3 (bata)

e ( thata)

){ (kappa)

"u. ("1\1)

V (rl,L)

Tf (pi)

- lIt.1ll vat.er la1'e1

•

•

•

•

•

lcnwlt.-H.1U1M' ndd III'LU t.rarurpoJ"t. ~oc1tr at. el.ution J!; n ./ sec .

efteeti1'l! nuid mua t.rantpoTt "lIloc.it.y. tt. / aee .

inatantatlll!'O\Ul nuid parUeJ.e 1'e1oeity, f t ./ &ec .

• :1ruItant..aneQUl nu1d ~r;l. veloehy under er.at. of va" l . ft. / lee.

• :1nttanlaneou5 fluid particle Velocity under troulh of vav lI . f t./eee .

• inatantan801.l1 eedi:nent vII1oe11..y tt. / eee.

• nit !leCUJalnt velocit.,.. ft./llllc.

• buoyant va1ght ot slIdimant particle, lbl .

• ooonUnate puallel WI beach. poaitlva in di.rect1an of vavi prcpagation, (t.

• ooordinate nonul to channel bottCIIII , or1p.n either at S ."'.L. cr at. uppu- ed&' of !"OI.lgbnUII particl a . ft.

• dopa of bu.cb

• 1n1Ual Ilope cf be.acb

• a .Iallurl of lhl vertical lDt-ent of meO\la eff..::te under a va"l , (t.pl.

• wlva pha3a &!\i1. , rlc!iU\ll.

• ranecUon coefficient

• d,yn-.1c n.col1 1..)' cf nuJd, lb,. sec/ ft'

• kin .... Uc n.co&1t)' of nuld, ft2/ uc

• 1. lb15 ..•

.,

p (rho) • IU.II. density . ~1lI./tt)

cr (dpa) · I.!I&'l-lar !r.qu_q, raM...:

q) '(phi) - angl.. of riipO •• of tu bed~part.1c.l. I17n_, r..:U.&Il.I

1!QQn.a It..: CHAtAC'n!IUSTICS 0' SAI'I) BI!I£HBS

IIf THB O'PS!plI ZOMB

" P. 5 . 1a,1.e_. B. Glen_ .101 J. A. Dnc""

M.ua,;Ju ... tt. InUitute of Tedloolo..,.

TIIh uport deec;r lbu I theoretiul and exput..oh l hl..,ul.pHon of equllllwh_ profile. ud 'edt."' lOftin, in the ofhhoU ...... of ......." bc.cht. . The iD...,sU,ation .... duiJl'ed to lut the .ppll­"hUH, of IlIUtiD.& ldea l l.ud tlleorlu t o the IIredkHoo of eqllJtl­brlu. c:ha ... ctlrUHca of lIbor.t .... ' 'Ind be.doe •• Two dlffer"nt "dt.ant .otion equtlibrh_ erihd. are eonsidued: the Uut, La Whi(b tbe _IIU on • ltallona.r , lIutlda a.re u. equillbrillJl, h caUId lndpleot .otloo Ind the "cond, u. Whlch the particle J& o.cllLatlrll wltb 00 oU ..,Hon , 1. "lied eat-bUst .. ,,!. ..,U OII . The IlIperi.Jlelltal I!qllip!ll!!nt couhted o f • 100 foot lone , , 1 .. I -WlIUed _ .. e hok coonininc • blllkhcad-I,pot wave .. chine .nd In expui­-entll be.ch. Por the profile experLQentl lhe belch con.l.ted of I well-lorUd. hip.!, rounded .iHca sand, phced It initllll, COMlo.nt &lope . 111" l.nil1a1 .Iope. Uled Vl!re I on ;10 . 1 on JO Ind I on 4.$ .nd the incident WI~ tteeplle ..... HolLo . un~ad fr ... O. O;U to 0 . 0411 . ' rofUn ""'rt .elSuud .t equHib6iJJ.a. Por lb. Mlrli,,, ","",- r llleoU the buch WI' u.per.e.ble .nd rllid but _. co ...... ltd with s fine La, .... of r ounded 11I1CI """ bnln, known inithl Irul wellht and l ocal IUe d11trlbutlonl , Wal,M and .ba diatrlbutlon. were ...el,"red u equiltbri ... for incident wa .... in UII! abo .. 1t tinE" . Results indicl t e the n.l.ItiD., theorie. to pr o .. lde 100<1. q ... otitltlve pred ictionl of 1) ae.wutl lu.it of proUt. .odiUclti(ICI aDd 2) w'bet-ber I siven bucb will build or !!f0cl1t under the actlon of • Ihen lncident _ .. e , Qulntttatl~ pred l edOll of pr oHllt .h.PIt 1.1 lnod 001, near the orr.hore "xlre_ of proHl1t 1II0cHliclUon. tbe lOftin, a"puwnt. bllr 0111 the QIIIUtnh. tbe"etigi prltdlctiClII' of In ina ..... in .IM IOrtin, in lhe oll.hon direction Ind I teodem:y toward tbe for .. tion of bl...-.11 1 lise- fuquenc, diltrlbutionl , The prltdlctltd Lacr .... in .un dla_tet in tblt onshore d irectioo Is round (ICII, nell' lha offlh or e: l u it of 'ortinr .ctlao . Purthar expuUoent. In lIIteditd to t1<tflne It. err.cl of lbe bi:eaker, bott_ fOlJlhnell , lind rip.­ple. aad 'hClIlIJI, depthl on the ""lcal dlsuibutiCln of fluid ..... trln'p<lrl nloc.itlit. , the lullld ... ntal q.U.,uit, Clo which the tbe:orJ.c1 ue blsed.

I

1. lJITHOOOCTIOll

TIl .. ~o: to:re .. a .. rted 0:11 botto. .otdUoaDt paniel. dlI .. to nlNl"-botU. orbItal n'll14 ... el.ocIUM ....,. 1n1tiat. and Mfnta1n ~cillato'7 .. t.1on o! be.,;h ~..u.lnt.l. u aham b7 I~ .. and Ea&1ason (1) the _'I. "'UIHI in on. v ...... period ot UIoIt .. ~e t ore", ... laU ... to tile _snitudt or th .. &ru1ty ror<: .. 4eter.1nea tile W.teIlC. and 41rIct1on ot the ... '1. .~t ... t1on.

Mod1t1~t10/'1 ot lHIaell pro!llas and aorl1nc ot beach a~te .... t.wo -.Jor noSlLlU or W. II'" .,Uon.

it 1a the pIlJ1)C»" ot 't.h1.I 1nvHUpUon to It.uct:r the applleabWtr of a:iJIUlI& theorI ... of DOlt l..u.nt .. tion (2) to toM. pre4ic:t1oo or tbe pro· ruM and IOrt.:11l& caar.atar1.nlel ot .and baaoh.u ir. the re&i011 ... Plrd ot .pprecabla brewr Whence.

8, Seop! ot u... tm..t.1pUOIII

FroIo tM aotehan1ca ot tht v.y ... 1nci~ llIOt1on of d.itc:-.te tpherieal bottoft .. 4t..nt., 1:11&11100 and. 0 .... (2) .:s-aloped uprtouloM ducr1b1J1& the relat10nahlpe betveen .Id_nt 41 .... ter, local v ..... char.etcrlaUce and local bsaoll tlept and rou&hnelll tor tJ'l. eomi tiona or:

1. Inaipient Md1r.ent lIOt.icm.

~. Ett.abllihld \0I01ll.l.ting) IedUoolnt. IIIOtion.

The ... nlat.101lllh1pe 1nclu41 no allow.""" tor .od.i!'ic .. t1on ot the .M.u1d torcell du .. to naar·thOA phoIno.-n1 lIucil .. rip ourrsnU, littoral CUM"lnt.. .nd brukaMi anc! eona.qu.nt.l.:f ani ilmt.ed to t.1Ie ·oUahere" lona ot t.h. be.d! pretUe bet._n t.ha ...... rd um.~ of " ..... - 1.nduced bot.t.o. .. d1nmt .:oUon and or _pp ... o:1able b .... gr 1ntlu.nc: •.

The I"Sl..It.1OMhip wo -.it IZtT cOMideratlon ot bNcb per-.tabWt,. • .-nd dppla. and. partW .. ilIt.eractioll IrIIi ....... u,. -Jo:r .. fWlpt.1on that> the ..... in~ partiol .. M1nt.a:1lw an o.0:1ll.I.to17 .,U"" a!vtp, 1n eonu,ct. Ir1 U:t the .....

the pJ't"'n" .t.uct:r t.a c.dcned to detel"ll:i.ns to whU clecr- u... abaY .. f1n:l1np aay be utan4e4 t.o the pred.1et.1on of protUe. and .Id'_at. aue 8OM.1.II~ of equ.1.Ubr1\111 .ancI bs .. cbu.

Thl labo",torr protUe uperaenl.a IIt1.liKed. 1n1U~l,y c_tant. aloped beadlu ecapo .. 4 of .... U aorta4 (nearlJr nn1!Orlll du) land an:i nr1crua 11lcW.nt .. ..,ea.

':be l..Iborato..,. IOrtin, uperJ..M.nta ut.W,ad a thin h:er ot .and hal'1J\1 • bl:08d lUll! d.latrlbutlon place4 011 aD ~.ble beath "f fl.aed .... HIt ... dope .

lqul Ubi: 11_ "ltftd,1 tiona ... re deteraincd .. u .... U, br .pparent U .... UOCI et ... t Iud ...... M .. ' .flu .. 1en, •• lSO hours of tenln&.

2

A. Eqlrllltn1.11111 s..cb. ProtUu,

Tn c:~e:r .:It-ion o! .. edWnt.. on t.eacM. b heine .tud1ed b7 nrlou. ..... u.rch VOUpa throughout. to .... world. n-.... group- .... appro..:'hinl loM pl"Ob­la. or beacb procea ... rn:a IUIQ' ditt.nnt. vtewpoi:lt.l.

Sa.. 111T .. t1p\OnII .... Prl:aril.J int..n.t.ed 111 "t.ud.7ifll: bucll procUH:I in tM plan view - t.h&t 1.s, parallel vtth tbe coast line. H. 111 Ht'Opsed u...t be"c:he" reach aD equ1Ubrt.ua ab&ps in tJt. ph.D now ...:I taDrWr (J) lip­pl.i.u the t..nI 'toq1.Ill.1brl.ca beach .. ' to thU .N.pe>. UuUch.r (Ii) .-ria .. the fa<:t.onll det.emlnlnl eo.utal. .. ~gy, or aht.pe, ... " ."", <:'<U"nnt.l, nbl.rial nIII-orf, 1n1'UtMUon, rrou, ..:tolon, wind, chudeal proc:.UOII, and blolopcal t.eto .....

lohMon (5) -.1 .... "t.ad:r to d.te~ the .thet. of .to ...... reS\lUto.,. _r1c8 such ... d_ on the ~ or 11...:1 to tn. 01 ... :'. and on u.. .tability or Oil' oout Una. He el.aeai1'i.e • ."." 110=" U'

-' )o!.&JOT stre:a:ns

2. S..u .. tt'NZIIS • M """ . ), CU! ! e....,.lon ... slidee

,. OMtIo .... ., .. _tlt or und b7 Q,", lIctiDn

S. 1o'ir:d action.

th, .. "" 1.,.1...,. 1U'e:

2. ~U81 into lIw.arlr .. cAD;TO""

) • .l.ec .... Uon a,Unait. Ut.t.Q .. al barTf.. ...

4 . a-vu o! .. nd tor eonu"nlct.ll11r1 puTp;>II ..

,. Io'1Dd. action

6 . Abraalon b7 "n. anion.

KalV otJitor invntlptonl hn, .~<:I be"eM' in .. cro •• • •• ctlonal vlew, They ,..copt.1Id that. the beach nbt&1M WI equ..UlbHUII pnof1l.e .nd tha'l. .t l.ut u_an1 nf .ppncilbl. breaku WlD.nc. this profll. 1& cnno.u up­wanl. ... Ippen and Eagle.on (1) nbae ...... d., tbil equillbrtua con<liUon 18 rQ.cbecl wbbn IJa .borevaJ'd net. nu1d. fore .. on nch .ecUMnt. parUcl. are bIl.anced. by t.he oppo.1ng gr.1'it..t10Nl fore... The beach in this prOfU,

,

1'1.,.. U d.1rtded 11Ito two ,UIUnet $Onel I. lhown in rieur- 1 ,

1. TIl, .... 1'1' 10M or th. iMha .... cone. Th1l reKion 1. Wi:wd ... t.l\e.t part 01' th. bI.ch 1.711111 bltwe.n the eU.bo .... bU"Ol and !.lui ,"lrI·,", ..... h 01 th ........ .

2 . ",. ehoaUnt wsw or th. ottlhon SOM. Th1I .... gien iI d,I'1oId .. that pIort or the be.ch lT1nI ...... rd or the oU,non bara.

Qt.h'l"I d1.~ ,UIllttJ..:r with thla cW.iIlc.tl.oll . Itiller and Za.1&ler (6) include W br .... ul' H .. lE .. I third l onl ..till. H~&JU (7) divide- t.hI i!>o-.he .... into the .urt lon, .ll(! the I,IpN1h 1(111' •

.... t.hI buth pl'Oru. 1. di .. ldo1d into •• pu.t.oe &01llI1, .0 hi .... in""U"lIIn concent,..~ their erreZ'UI into .epar.t.e SOM.. !'be lnehon 10lle hall .tt.r.e~ rlda .ttenLion .. t.hlI u thI raa:Lon 1Iile1'l tl'A l1ttoral OT lonphol"l enrrem.. ocea:r. u.o, it 11 t.hI ",lon oC the "".t.Mt t.J.<r~lanc. duto to b....n:r aetlon with 1./'&1 _untl at .. diMnt be1l\i t.1wn up in IWlpeMlon. Mooot oC t.ha llI:r_

Y"J'I 011 natural. be.chH .n t.".n in t.h1e acton .. lt 11 d:1U1cult to vork in the o!t.m ..... aona.

SUVl.teT (e) s-rl ••• OlrT'IQt Imqwl.q,. ill UMo r:1.l.d or couw .ed.1-l1l8I11. ... _n~. Be obi.,.... .. the \lll1IIl <fbi.1100 or oc.an ....... ilIto two cIU_ ~inet t7P", .to.,. ....... and sw.ll . S .. ell ............ chiracteTiltd by ....u ... ve hl1~tI and lone wa .... per1o<U (1. •. , .... U H raUoI ) , while .tol'1ll ....... ~ .hort and. lte.p .. I ..... (1.,. , wp ~ raUo.J,t The .. t.wo ...... typeol C.\III' two d.1tC ..... nt t7pll or equillbr1.",. belch proru .. , • av.U protu. and. •• to .... pronle . • .... ll protU, iI ~ct.ri .. d by steep bulldfnl belchel whil •• • to .... protu. 11 n.t and. 'rod1nC.

The ",.U pMlfil, 11 01\1 WIIlch reevlta trOll! IlIdian!.l blinll tr&n8pcrt.14 t.owa:rd.l the .ho .... by th' ... tranep;1rt ot ....... , I're!1luallJ" tol"llinl III eqIl1l1briwll. protu • •

St.anI protUea, &ccord1zl& to SU .... ter , ..... tOl'Md lircel.7 bee'UII the .bort.er penod. ltonll ...... quiclcl.7 I.tul"ltl th. toruho,.., Ind brlnl t.hl ... te,.. table pr.ct1e~ cO~lIci6ent w:Un u.e be.ch IUr!aoe in tt>. '10111 or uprolh, Then the retlU'l'l now crt t.he be.ch equili the ..... 11 ot UMo w."'. up OlltG the be.ch. 1'hi.B I"Ilul.t.a in • I"llitll'1lJ' 1&1"" l\Tdraullc jump arid • ceneequ.nt h.1ah dOflTM ct .I>d~l II'Itrl1nlleDt .. here th ... two ne .... _1.. Thi.a II\.t,..atn.d, .ediJt-.nt 111 c&:r1'1ec1 oCtlhol"l wh.re 11. iI dapallted. and aane! b&... ~ bullt up . 'l'b"1 o!'taho,.. bani bl"N.k I,Ip IUbllqu.nt .tGnI w ...... and thus redu.oe turther en>aion.

Johnson (9) obl.1"'O'$d tl'I .. , two tnH of be.ch prorUH and clulUi .. tile .. Uh relpect. to the foretlhol"l elope .. 'orc1i:llTT" and ·.tor-." profil ... In labor.to..,. ItudUI hi rO<ltld that !.hi tleillltt-lInctb ratio of the "'Vel and not th.l orll1nll be,ch 'lope i. t.be iIIportlnt f.ct.or ill clet.ar.1ni.n& tt>. chAracter or t.be equ1l1brlU1!1 protu. . the 'ordl.:lall~ or • .... U· protu.a allil,)'1l fortlld 1.!! tllot ...... tank when t.he l'IllUil of t: (the deep ... te r hellbt.-

•

0.0)0 , ato l"lll beach .. aly~ tlu ..... d.

tor ~

'. values greater than

Scott (10) wo obattn'ed u...t vaYell vith a n. .. pnne ratio greater t.han 0.030 produce ·atQ .... • or ~v1nter " prat'1.les. wh1le thole haYin& a steepnella r.Uo 1 .... ~ O.02~ prodIlc..s ~o...u.n.ry- or o._r· profUea. He .t.trl_ bqt. .. UIOI oUsho ..... "_nt 01 lIed1--n1., durlJII per1odf. ot Mp wafllll, tQ 1ne ....... d turbul.enc ..... eloped alon, the bot\.cIJI by the Maher va ..... ".

Scott alIIo II\lUWIU I IIoIt rurlJ' 10111 froIn. ocnn buChel III steep .. ..,. , ..... ry the lIe<1.1mnt ae..,ud 1nto d.pt.hl .. htlnI the INll, genU, vayU c.annot retum it. tQ the beach. 11111 11 .'pecially t.ru.. vhan llUt.ar1rle canya"" co ... clon to the cout.

Rector (11) , lilce ether inveatigltoMl, .... coc;n1111d that .. ..,n et gr.ater .teepru!u t.nd&d to &hap' t.h. beach to a natter terellMre 'lepe vith a bar 10.-d at the breakitl, point ef th' 11. __ , whU. lon,er and n.attar v ..... .,ved a relativ.lJ' U-atu Tolu. or _tor1al on to !.he lor.lho ... t.hv.s pn;o­ducing ateeper oUaho ... beachea. Ha fPeII l'urthttr by ob .... rrlnr; tbat .. tM aand ai .. rel&t.iv. to !.he deep "Iter va.,. 1.nJUI t beco_ larpr, the &and

... _nt vu on to tNt lor..hor ...... n \lith u.. lteeper 1I1Tes tMted .. Con­Vlree.l:J', .men the aand vu 11M, re1aU .. to tb. vI"e la~, he obtl.ned that. the -.jor .,VllDll11t ot sand ..... .l.lI the oU.be ... 41.rIcUon,

ThU i.B in _,"_nt 'With !IUco. (12) .. ho fOIlM thf,t ,te.p natu:ral beache' contain ceara •• and wh11e nit natural beachn tonli.t of tina aand.. Buco .. al.o noted that :natural beachet .....,d. under "ton. wavea and natten lihUe a bu11din1 beach "teepeN! und.r "quillt" W1I.VII~ ..

It .hould be not.-ed. thlt the oba ....... tiona lUcie bJr t.h .. , In.,.,,tigltoMl .... qualitative in .... tW'l all little ill Iwovn ,bout the _chanica or .ec1U,otnt .,Uon in the inlloore Dr Ilirt IMe.

BI&nDld (l3) point. out WI. 1Jq1ort.anee Dr t.h& oU.ho ........ gion bJ' l¢nl, "In • lIrge nuabel' or pl'lICt1c.il. prob1._ on cout .ro.1Drt, the 1Jt­..u..te inshore Jlb-noaena 11 controlled. bJ' the eon!'1curat1on and hT 81"" ., • .-nta ~ grelt .and aeClUlUl.UolUI vh1ch extend under shallow w.ter tar to .. award or tbe brelkert."

It w.,. reco,.nized that 11 belch "v"","nt. were to be undlretood, .0 ... knowledge cr thl mech&l1io. of the .. d1Jrto!nt. IICtion would hlye to be ac~.

Thinkin& along thIn linll, EiNStein (lli) prapo._d &1'1 invIstill.tion into the I!IechaniCI ot IfIOVlment ot buch sanda. H. SUUllta t.hat tho! bea"" • ..u-nt lIf)t.ion be expreuld in tel'mll ot • turbulent eUllp'neion and. • bed­load IIIOTttaIIIlt , &nd. that I. bed-load tquat.1on tor belChe. be deriTed.

It 11 tnown that water pl1'Ucl.1I .... tranepon..d in thl directioD of ... .,. propagation due to tbe .... transport .!tlct. A paTt1cll dou not

,

e~lete ill dozed cmuIar orbit. but &Iter t.htt punp or .. ell Viii .... it. it' .on<:! ill • ...u dis\..anta up t.1Ie beaeh. Lon""at - lIili1M (l S) derind iIIQ -.que-110n ,{"ins 1Il ...... rt.leal d1.IItrlbutlon of nat "-iII transport "t.locit.,. .t the batt.. I..r! • CIl.o5.d clJanne1 or constant dapth. The IWt ..... tran.port n-10c11\1.t. c1".,n cmpth:ln<orHs .. u t pte ...un.

Ippen e.">d EiII&lllSon (1) at.udied the .. chanica ot tha vaVll _induced .oUon ot diecrete IIpherlclLl bed particle. and t<)Ulld t..'Ie net lediMnt .01.10" to be eWI ... to t!'tis flu1d .... 1 1r&n.lport. 1hc7 r ound. the direction ot nn 1ed1-.. m. ."tlon. ~OVUTOr . to be detcrm.n.d at IIlI1 point. tor IIlI1 CiV1ln partie!, .\.&0. hT the nslatlV1l -wdtuda of the Va"lhUonal ro",a &nd u.. n.to ( ..... TiIIgfI 01'"lll" a "a"a ey<:le) nuid to",I.

They Nt ro.,.tlI ill cu .. UlcatiDII oj' I~nt. f'II)t.lon <kfUl1n& 1ftc:lpient and .. t.llblis~ R8d~nt .otion .. fOUCII'l1

1. Inclpie..'1t ~"t l!ntlon:

Thill ill iIIQ U:at&!lt.en.ou.a eond1tl.on reached when the r .. ult.e.nt of all act.1 ... to~ .. on the particl e inUHaets the l1rIe eonnect.ing t" ~-p.rt1.<:u eontact points. (J.ll rOI"(:M iIIct1.ng With the l:ICeeption or reaction rore.e at tJ-.e bed u.. ternsd ~.cthe.")

2. Enablb~"d 5edu.ent ~tlon:

This l..II .". o.cUlato.,. Or quael-oeeWatol"l' eond1tion ot ."tion reeche\!! vh.n tor lone portion ot .ach ....... c7l:1. the a\lIII ot t.he 1rIet.e.nt.aneou- acU."1 tore .. exc.ed.a thlt value nec"uary to inl tilt. lII)11on.

Ippen and Ea&!lIson (1) p,...,lI"nted an eJi:plrlcal corrllaUon of loct.l .. av., characterhtica and s"dl!11!1nt properUel d •• crl binl the IIIItabl1"h,d motion condition ot:

&. Eqllllib .. iWll or te ro nllt mUon

I.. Net " .. -"horn IIOt10n

and pointed Ollt t M fllIisteoclI or o"t otE'hor. IIIOUOn &lao.

Ealla .. on. Dean and Peral ta (16) vent ba~k aVar Uta aarl1 ..... tud;r (1) in ord.r to p."uerlt th., data in t..-- ot i'u.ll1ar phylIlcal nl&tl'lnllh1p11 lI'hich coald be jtlati/ilbl,y IIXtrspout.ed. to natural beach... The,. praeant a t.~lIOnticlLl anal)'IIu .. h1cll yield.. an equation lor the net ,..).oc1t1 or II pVln apherwll lIedi:nBnt part.icla ..... l'ur.cUQn o! a ndJlYonc. co.rr1c1llnt. Co. U-.. a!tectiYlI nutd un tl"llJlDPOrt. velocity Ut, and tha ballcb dopa ,C\(. 'MIla .,quatlon is verltie:! th.roucIl re-enlu.at,10n or the <kYo ot (1) and throll.&;t! addJ Uoul nlatr.! lIX)ler1a!nta.

In tt-.. abo ...... rer«>ea • .-ure ...... t.II or the 1:II:ipJ..nt .otion oondit1<m u.. .ao cOrralat..-d nUl aeyno1.d.ll IWOIIIber by _arw or a dari"" reaistanc. eOlltt1c1llnt..

•

!&IlIIOII and D .... (2) ~ var1.cNe ref~nu 1n t.he ~ia ot (16). B:T _ of bounduy layer u.ory both u,. .. t a~\ "loelc,- NIIl 1lIclp1ent. .,Uon Cl<prllUlonlt .... .xt.en6ed separatelJ' to t.hoo pr.d1elUon of tt.. tqIlil1_ brl_ Nl.at,loneb1~ be,,"en loeal ....... o:l1arao:t..r1.At.lea, bot.t.oa alope IUd _1an pArticle cl1aMter found on tlAt.ural ~"I.

othar lmMUpt.on w!lO 11&" at.ud1ed t.he .chanic:1 at Hd_nt. .,UOII tlftCIlr an OlIcllllt.1n& nl.lid tield are Li (11) , ".IlIOhu (lS), IUd KIllkIn1a (19). TheT IMoW-Toed a bo..uon\al plat.e in a atW auld and oblarT&d ton. _tiOIl v1UUn the bowxla.J'7 lqer. Their a!fort.e vere o:oncant.rlted pn-rtl,y on de­fillills U. oond.1tiona tor '··lna .... t.wtW.ant tJ'&IIIIlt.1olI ot t.ha bottoa boundary lqar lind an ~eal. dat1:dtlMl ot tJla cond.11-ionl tor 1nciplent Mdiaent. .oU ......

B. Sedasnt. Sortina:

In. addition to thfl nud,:r of belCh pro1'Uaa and bov "'-" IrII tor.oi, .... rlO11S llIvelt.ic;atorll hi .. c_ntad UPOll t.ha .. leet.he tort.inc of IIdu.nu on beach.. . Sll .... tar (e) noted in awrnari.1nI; tJlell ob,ee .... atlont t.hat t.lIe nnd ".u.s beCOlia 10rt.&d under Va" action, u.. larpllt. beina tlIl"O>III hi"" on thl beach, r1lle uta:.-ial being loclted in thl 811rt Kone and Use rinllt &p­peaT.in1 bercmd H.

8a-=0III (12) . in h1I ,tlldiu or PI Citt" Cout. bllchll, round t.h&t. t.he c1U­trlh1it1on or eand alonl a prof a. 1lId1Clt.a1 that 1"-&1 gra1nI .... tound at point.. ot ..n.rum tllrbo.>lenco and thAt. &q11ll1brlUII liue get I .. Uar ... tllJ"ta! ­l""'e docr-..-ea.

llIun (20) . 111 I iI .. ner&! Btvd.T of .... dl.JMnt ..,rtina, poat>.llat.. tllat. vnd,r w.v81 of IllldiWII int.anloit.y, eOane Murial will ."va IhorewlU"d by th, rapid lurS. u.oel.ited with t.h' Wive cron, and ti,. l\11.erlall, which hav, a aralloU tendflncr to bIo in .ulV-IIIIlon, will be lrAnSport ed 'liward by ~1p currllnta and atli!! bot~ 4rl.tt. He rurt.her sht.e, tl-.. t. the ... 11 IIv.,.. I ,and 'iI, for vtI1dI the net trlNlpOrt fa ,oro and thia _\.ed.l .. ill bIo the predo.uu.te forubore beach ut.erlal and 1t. will bl locall;y .. eU .ort.ad.

Illllltl conclu<:k=. that the .. ia a definite eo .... lat.1on botw_n tho! dep"'e of lortinl and the _dian di.aMt.er of I o...u.nt .. ",ple.

s.t.o (21) develope an oquI\~n predict.inS thI rIIlaUon batvllln ...,an aacU­_nt <U.u.ter and the cr1t.ical fil.lid .,.1<Xl1t.:7 !or Int.rdronlnt. by Wlvel or low .. teepn.,,,,_ In lli d_loprlent , hto U,\WI8 that. LhI ah.aring tOf'C" on tha 'el bod .... C&lUIed by the -... veloclt:r of ... vo ..,tion and thAt. the IIltIrl:J' a.nd per10d of tha .. VI rl!ll\lin COnlt.a..,t durinl ito propaption. Ife eontu. hiI theory b:r 11bol"ltory experiJolnl.a 1m b:r nat:>ral beael: ob.!leJ"'lIUo",_

Ippen and £aglOlO .. (1) rtlalonl!d. thlt. t.he procell >6ictl p .... du.c .. till net IlIod.J.Mnt. _tion the}' obiervlKi, 11 I IIlICt,lV, 0"" beclllI.e ot the eritical rII1aUon,hip bIotween Ulrit.aUonal end nu1.d Core.... for tJ\i!I re"on the Itllpar portiollll of oqullibrll.la beaehel {>6icb OCCII"!' in to ..... ot 11"1'111' !lilt

,

n\l1d torca.) .hould ~onU1n larger IPIed1.an d~t.n tlarl SO"". baTin& nat elopes,

Th1.I, tbey nna, .hould prodUC. a &r&datiDn in Nd..1&1l. particle d ie .l"Y'cn coa~a to !11la 1:1 a u8'IIal"d diHct.1on ill the o!'tlbo", 10l'1li ot equ.lllbril:al buchu ,

H1.l.lar and Zeigler (6) Itudittd sadiMnt 10rUna 00 n.ato.ral b..c:h." cor­ralat.1n.g t.he:ir obaw-UOnl With the tJmo..,. of Ippen and Eag.l. .. on (1) . Tba7 propoaad two ~tII!Iea, 0l1li 1dU! rD .eavard HdiMnt. .,uo~ under grav1t1 and. ODI nUl bo1.b landvard atd --.n3 .,t1o~, Ttlq totWd thatr /WIt.ural baleb obee .... at..iona: to .erel bettlr vl1.h thI tirat .odll. nt.ratol'll, they concllldr.1 that gr-.v1t;r ~ -. .... ry Utili part Ln ~rln& Murial.e ott.boN,

8

,w,

• . '.

I BREAKER REGION • I

" •

. ~ 0.-.-....... •

S£AWARD £)lTRU41T 'I' 01' Pl<'OflL£ MDOIFICATtON

'­'.-- ' '---' ,­•• •

Nolat.1on Der1nl t1o:r, S~.tch

9

In.

c •

1'1s. 0). Foree oerWtlon Sk,tcb

.... Equllibrilm Seachn

1. a.c~und (rn. ReI,rellCu (1), (2) e.nd (l..6»,

.h • 4 •• p-vat.er ~ell1.t.oTY ...... ~v .. into ehoeHn,,,at...r, • 4apU. h _nt.u.all:7 re&chltd at. whieh nvJ.d p6M.lcle _tiona .... inchIc"" "",ar the bott.o.. OnDhore o! tbi' point the .. fio.U.d velocUi •• -...d. !.heir ..,o,*­P"JVintI o'~llbt1l!1 preUIII'II p-adilnt, t,.,eo. _ ... 1lIt..-nu. SiaUarl,y, the .... 1 .. , .. lnaUntanaotUl h1drodJ'nUdc Cere .. .x.~ en WJrldual bed e.diMnt. partid •• will inc ...... oll8he ... of thh point.

At .OM point tn, 1netant.an&oue ~c tore .. .." b.oo­nU1cllntJ,y 1& .. ", to CIII ••• taU.a iMtahUlt1 or ,ecU.at parttcl .. ot • &i .... n ,h.. Th1.I pDint. u c..ultd the po1tlt. or llIclpl.nt .. UOIl tor that. • ...u-nt. Ih' tor the et"n bcMi-part.leI.. poMtr'J' -.nd ~cb dop", !)milo ... or 1.11111 'point t.hat put,1eul&r Ih' w1l.l be in ol<:Ulatol7 or quul-olcll­l.lt.o1'7 .. toion. (Pro1'1de-d U. beach .lope 111 the ._.)

'0

It. __ posdble that. natursl buchel adjuat t.belllol" .. to • chanp 111 U. l.no1den~ vue ~ llet. led1."t. t.rUIBporl. vb1eb. c:ont.1.m,., Wlt.U locll. 010,," and .ed1an ,and ,is .. Mt.1al'y ... e.."me,.. t.t.. cond.1tlol\11 for incipient. .,t.ton. TIwI IJ'\ equUibnv., co.cdi t.1oD is ruched.

'or IIlI(! of • eOMt.ant. .he, uu. c r it.ar1on for toQUllibr1.lua be. ehM \I01.Ild lII¢IQit.et.e .t.eepeT 110,," 1n .hallower v.ter . FOT be. chea o! ~Olllt.ant.

.lope IqIlillbrllUl d i u VOtll.4 be ~ ~ ~04r .. t.o fine 1n the . .... nI d.1.re<:t.10l1. t'1111 behiviOT is 1n quaUtlt.1v" acrl a.mt. Yit.b t.bl ObeirvaUOllll r-.port.ed 1n S.cUan n. WI call thU t.he !neip1lnt !1at.1oa Criterion (or oquil1bri ... *011 .. .

.. pIl"tillle W1ch is 1n I nll1d Y1IlOC11.7 fill.d. It.ronceT t han t.llat .. .,..e&:7 ror u. 1ncipllllt. .,titm of that lise, is OIIcUl. t1na 1n I ..tton cilled Mrell'l ·ut.bl1shtd" I~t .,t1on.

The d.!reCUOCI and .... gn1tllde or UI. net __ nt of ~11:1"" 1n .. tlb­U,bed el<1iJrlant _Utln depende on the nlaUn 'Rl.1l1 of t.hI OPPOI1ni Oo.poMlnte of the CJ"IviUUonal fllroe, 'Il , ....s Uuo nat ( ... IT .... onr I WIVe O7I:le) nldd

forel, ;" , 1n I pl&lll parellil UI the 10<:11 bllloll elope . When '0::>'" , til.

Nt _Uon will be o!flllono Md vIIIn '0< Yr thl puticle vill lIIO"e oMhon.

When '0 .. ;, the particle OIoWatM with no net. .. t.ion. I"or be. ch •• o! COliltant lloP'! t.hU CIlI be lholm to be I condit1on of llI'"tabll equll.1.brll111, but tor til. prlOt1eal 0 .... or poelU"e I l.OPU incl'lllllillf;; toward tn. loon, U. nop","ntll I ,tabla IqIlUlbr11U1 . If thi •• table equ1Ubri_ u:Ute 11aII.l­t&nlOWI~ It all po1nY alone I buclI i t. Can be 11111 to &I.o p1eld _tNpar Ilopee and ooueer IIl'Idat1on 1n the onahono dinoction. VI clll t.hLII the EatablisMcl l'bt1on Crit.arion for «{\IUibru. buchu.

Do dUoer of the .. tY'Q crlyria, or co-bwtlDlII oI hoth, IO"'IrD u.. IctlUll OQlltl~tlon of Itqll1llbrl_ -n.. ...... ? 'Ih1.I _twq i_ d .. d .... d to ll\II_ r t.h1a qllllt1.on.

2. Ir.clpilnt l'bt1on Criterion,

eo .. io:\lnnc I 11DClI epbi"' Oil I bed ot aphe .... II mown 11'1 FilII" J, t.Ilc1nC _nt. of t.ba drla , u.n., Imort.il, p2'lllIIUre and. p'arlty foren _bout I JIO lI'It of bed-particle con1.aCt and. uea1r.C thf,t incipient .. t.l.on OCCUMI .t a phaII. ancle oL 9(lO or 2700 (1. •.• 110 inlrtW 1f1'flCt.II), &a&luon and 0. .. (2) <kt1nld u.. cond.1t.1on or inclpi1llt. .. tlOl1 br'

(1 )

1JI IOh1ch V.r 11 thII wt.ant.aneO'll nv.1d ~1.cl .... locU7 It I dilt.anc. eqIlIl to tbe pan.lcla di_tar IbcmI t.he bid. '" 1e u.. M&le or "'JlOH oI t.ha bId-putlcle .,..w., D u the .adaent. ~r and. S. and Sr are t.bt lpadtl.c lP'arlUu ot the I~t and nllid nolpectblllS.

"

It.e ! s1&n 1f; to aecount for Wtlal "",Uon in t~ .. 0",110" Ct, e · 9QO) or ofi'B'ho=-- d1rec'!.1on (.,e . 27(lO).

~ Eq.!l)f.Ild, re.coi/US1ll& ~.at for .cHIt practical "allWa of 0(" COlI g( • 1.,

At low Reynolde nllfllbel'8l

s · , "

1 • Bee <\> •• 65 tan iQ

in wtw:h the :oTlln.ant, N, U .. !'ultetion oj' bowxkry conl11t.1OI18 ;IlId,

(,)

(,)

(4)

In tile :ase oJ 1.nUtre.t. hen, If w1ll be priJgrll7 a tunotion of p&rUc1._ .b_~ and boundary Pro:d.a1t1 for I.IV" It1v~1n ratio at p&rUCh l11antu to bed 1'aII.S/' •• neu 1Ie1gl1t, D/

k• For 'FAnl ralUni an & ~, • ...,th bound&l')', c.rt1 (22)

found the ZlIrIII <It linear dral: to extend to .. ~ Reynold.ll dUllber at about 100.

Haugh (23) s1na tlle ....uoc1ty 418t.r1but10Jl ,,1tlliJl 11l11inu boundArJ' lllyel"ll under oacilllltory wave. u,

Q..-PY ,in (e -f3Y)] IS)

in 1Ih1cb £AT- 1& t.i'A 11101'"'' auld part1cle 7.J.0c:1t) at. the edg_ of the boundary

l .... er ar:d "'~ be vriUan,

, .,,, (6)

in which 'J 1a the yutict.l cOQrdinate MUurld up from tt\4 batto ... and,

"

(7)

111 Eq. (6) H1 and R.. &re lccal 1nol~nt arwl nfltet.ed v .... he1&!zu r.epee­t.i1"l)". Equation (6) e.1l btl >Irltwn in t~ rom.

in which X, U. ran""tion coe.ffiotent tqIlall H.. .

"1 Auu.dAC the ,rrecu .. inatant.&Mo\l.f nuil!. fore .. t.o li. at 'I - D,

Iq. (5) N:f be .~te4 at e . SlOG Ind 2700 by,

1 \lrl- 0.86(' D ! I for .- 0.1 < (-> 0< 1

IIIIbrtitutl.Jl, r.qa. 0) , (h) and (9) tntcl Eq. (2) )'1,,1&,

SolYinI Sq. (to) for the bNch tlo\,* :

(I)

(.)

(10)

(u)

= .1nIX; . [0.'" V ,Ii) e "

( '; s. ) (1 . '" ~ .. " ~~ .,~~

. 1.3} 19.2

(12) • •

"

which vill ~ u81UQfd to be t.lwo ..... ~ COndit.ioll for .. nd be,eM • •

IIndoIr t.hot UWJqIt10u u..t. all ~.ct.ion of .............. 17 11 eonewrt.r,1Ad n t.be b~r and ne&lect.1n& "DUI7 d1ldpotion, U. ...ual eo ... 1d .... UO ... of rete of _1'17 t. ........ al .. ion lud to t.n. _va hditbt t. ..... 1'orut1on reblion­.bip:

I

H, 111 " ,

(1)

in wtdcb. ~ end 1110 ... the ehallow •• ter aDd deep "-tIT 1Dcid"nt. 'HI" t.1&bt.e rHpKU .... 17.

U111J:li Eqe. (12) and (lJ) , Eq. (U) wq be vrlU.."

" - 2$8.7 l>iui ,-

"', -,;-

-.,

"" -,;-

(lJ. )

(1$)

(16)

-l

!¥J (17 )

.I.. 1..11 lnd1c.t.ed b7 tll8 elternete .1Jn.t on t.he 11f t. hand dde ot Iq. (14 ) , incipi.nt. lN1ubUit.:y .q tl'woret.icaUy occur in eit.her the o ... bo,.. or oft­Ihore direction de""nd1I\i up<;>n the relett". lIoIK/lltude. o! the crnt-t~ugll ....... ")'IUHt". Inc! the 10<:11 bottom Ilope.

In rel.t1vel.:y deep ..... ter vhn" the >lavu Ire .. Irl.:y Bymmlulcel, in­cip1lnt notion vUl very likely cccur .1. e • 2700 -- l.e. , in the otf­.hore direction and. the Sip' of sin ex. IhQuld then be neglthe.

It t. quite poadhle that in lhaUQ'l/'er Wlur tru. veve u,..t". IMl' beQo.e ,"It enollgh to call"" incipient IIIOtlon w:der the Cl'Nt - i.e. , 111

"

the ,horewud dlrIction.

,, '" -,.-

, ... (" lr Sf

(1+co, ~ ) + C1. dn41] l II.r02. II.rt2]

-,) [ .'" (4).'' ,-.,,, ( ~-O< I] (18)

111 vhiah Ute and IItt. U. the inatallt.n....a n.dd parttcle Y<t].oeiU .. und.r th.

anet .nd t.ro\l&h .... pect.l .. ~.

AM is • pIl'UIIIt.er whicb de!1nea the direct.ion ot pIort.lcle IIIOt.1Do:I at 111-clp1ent depth. I! AM.(. 0 toM U1JlDtLrr o! the vav. u too -U and 1n1tl~ IIIOtion rill be 111 the otr,bo,.. direcU.on. II A M> 0 tIM u,-t..,. 1& 1 ..... _up teo 1JlitJ.a\.e onabo,.. IIIOUon, ?b ... prolM'rt.lu !;an be .-..illtd u roll ..... ,

.t:.. H > 0 oMbo,.. incipient IIIOtton

A M< 0 oCrahore incipll.rt. IIIOtton (Ul

Eq ... Uon (14) bu bien dlr:l.wd undlr tlII UIIII,pUon or a .,...t.rtcel ~ lOCi tr dut.r1bat.!.on.t.!:u.I oUlIloN 11I1t.tel BIIt.ion (nelnhl 11.D 0(.) 1& the onl,y c~t.lbll !o ....

n.. t\lneUon .!2 (d/Lo) inc,..~ ... 0 nlpldly rlU. decreulll& depth . how­

..... r . II 1.0 toJ'Ce the 1"111>1. band .1.doe of Eq. (llI) 1.0 ba...... po,it.!." 111 qu.!\.1 deep .... t.T". It .... u. to ha .. onJ.:r poa1t.tva baach 1l0peB, thU Mana .1110< .bould bI poe11.1 .. .

'III &h&ll tl:w.I .... cnl;y the po.1U .. • 1en or .in I<. in IIhIt.IYlr depth Iq. (llL) is IAll1&d. Th1e rill int.roo;tue. a -U Irror when the aqulUOll 1.1 e.pplled ...... U. ...... ard end or proC11e ..o1I1cltlon,

Vdn, tlwo coord1n&a ayatfml or fill . (2), Eq. (110) ...,. !.han be wr!t.t.ln,

(20)

"

(n)

SetU,.II& 1 · d/ Lo and 01(01) · L,,~ , Eq. (?OJ Mel=--,

1; . {.,..., 7, ('It. ) (22)

111 which:

~ .. ·"2 - .1.J6L. "'1

f? .. • . 12137 A1

B) .. - .00l62 ~

(2h )

( 2$')

"

e, •

" . . " "", c) · B:!"'. aB)!\

,,' ~ . [e,/ _ 41'JIIt] 1

(26)

Eq. (25) pr.a.n"- .... ~lbr1ua bQeb protu. "bu .. tn PCb powl. o~ t.a1m & condit1on of 1nclp1en't • ..u..n1. _tion.

to plot 1.1'.1,., proto.. for arJ7 ciftll beacl'l, it 1, n .... t n.c •• ....,. to dao­t4...u. u. _.nit1l" of "'1Lo at tJwo ....... ard .,;tr_ of profUe ~l~t.1o.n -

1 .• _, (d/t.;,)au. To obt.aln t.hiJI,Eq. (11) U¥ be .ob_ tor (d/t."l.u. il the

beach .lope, Q( • !II lIet -aual to it.. und11Jf.1I.J:be4 . or11in&l yr.,lue , r;I:. O.

,

To uptdi te this 1011,11.1011 f2 (4/Lo

) 11 plott.ed. v • .

j. !,t.blilhed Motion Crlter 10n

By writing tJuo equat ion of v&ve---induC41d ""eWeting .. tion for. ainlle .phertca l particl. COlIAU.rlni dra .. , p .... aur'I!I, lMrth, ~ ... nt ... u and V..,lt)' torcell pilla bot.t.a. l'r1.et.lon, and. lDt.egr. t1nl Oftt' one wan C7ch , £adellon, Dun and ?rUt.. (l6) obt..1Ded:

- -, (Ur - V) • "b 8111 0( (28)

"

6 .0

' .6

'2 4 .•

4.

3.2

2.4 1-~

2 .. 01---\

.6~-\.

o .• ~-+--f',-

I 15 20 .25 .30 .35 .40 .45 .50

"L. 1nclp1e::.t lIouon I'r'c!U. Fbnc:..1or., !'l(,~l"'. , !

10 Lo

"

11'1 vlUch nt 1JI t.ba ettecti .. nuid _ t.ranllpof't .... locitrj u......:! to act. .. t. , • DCa.,. n.. J), , 1JI w ruulttna 1Wt. .... u_t. nloeil.7 and ~ 1JI t.M

bua7wlt. ~t. ot the .Ml ant. particle ot di_~r, D.

L ",., 1n8t.an~ <S"'a ..,., bot.too. t'r1et.1.oMJ. tore ....... both line ... t'\mCt.1OM or W raU,U .. Wl.an~ nllid .... locHl (ut • ........ ).

2 . COrmu:U ..... cc.le ... t1o~ ot tha aer;tiM.nt pert1el_ .... neallC1ble.

J. The e1 .... Uon .. 1. which tIM atteethe inatlrltallllOU .... l.oc1~ and. .c-cel .... tion .ct 1e independent 01' thMI.

4. The 1NItantarltOU nllid part.lc.le "'lacitlY .. I. the I.dp 01' an:!. v.I.th1n the bot~ boImdar:r l~r ..... P'tVI re.pect1nl1 b7 IIX'pI'Mdon. ot the tOI'1l:

Ut • (j A., do q- t. • 20'"80 .in <I q- 1. • Eo

at - 1.1' .ina- t .. 81'.in au-,, ' Pt COlI (f' t • Qt COl <1 11"'1. • Bf

in which t.No quanUU .. A, n, P, Q end II: an independent ot tt.. and 11"'1. - Tr/ '2 under the waft creal..

5. The coef1'icient at .pp ..... nt. ..... 1& cOMunt with tiM.

6 . The oediJllant. part.icle. an in oacW.tory II'oCIUon dur1nK the entire w ..... paried.

~euainK that. the dra. nl.t.1oMllip ill Hn .. r, tquation (J) applle • ..nan :

Rl - (Ur • V)I) il

and Sq. (28) bee_,

,,,, Longuet-Hiu1m (lS) pre.ent. • tlIaoraUc.l .olllUon tor t.M au. transport.

valoelQi' diatrlwt.1on, trCl ) , in a clOilad channel wh.1ch .. t.1&1'i .. cont.inu.1t, . Within a l"'nu bottoll bcnincl&t7 layer, !.hill .olution b ciViln hI:

"

In. whi.cb 4t IUId ~ an U. 10<:&1 i.nI;1dent. IIlld r.n~~ Vutl UIplltud .. , NII_ pecti"lJ". '%he tIL"tCt.to~ r(p)(U) L'lCi r<,)(U) .... &1,..11 by,

()l)

(]2)

N8ar t.ile botto .. , Eq. (31) <:an be approJ:ilulAd b,.

()))

The par1odi<: t.IIl'II 2~6r :sin titr:a: r(a}(U) in Eq. ()O) U Ulro tOI" uro

"' ran."'tion. It. dd'u.. nloclt.J" .,ch>l.eUorw hArl.n& a teQStb .,qu&l to halI the loeal v ...... 1engt.h and it. aUu oal:r in t.be p .... _ ot ren.eted vana.

Sinc .. no nt.apt. u bain, ude in ~hU .tJ.Id;r to pnd1<:~ 10u1 JDduJ.at.10rw in b"ch proJ"u.., bu t onl,. _n prom ... , the • .eoad. I.e,.. ot Iq. ()O) vill M nei1e~t.ed.

Comb1ninl Eql. (2:9) IIlld 0) tharefor .. ,

("')

••

.... -.1.nC 1.11.1.1.,

2 (l-}~ )

&1.1 - »

,)6'

(1)

''''

ell>'

in lfh1<1h n 111 " c04lJ'f1e1.nt abllorbin& tlw .tte~tI or ~ .,oroett1 01 t!l. Nolle or .,,.lna parti al .. .

Eq. (36) ..., I'IOV be 'llT'ltt..,n,

2 • CIa · nVD • O.nn(l. )(: ) (7fl!1) CD ( ~D)'7 I.. 1II1nh2 2 'It ~

(40)

--,;-

In ds-n.1on1 ... to"", Eq. (1&0) become:

(U,

(;;.)' . ",. (4' ) .... ~, _

• 41'fd) t

2 2Tfd S s.nh """"["'""

("')

(.,)

(44)

(45)

(1.6)

~r ~Uibrl_ condit1.cmll t.b, " .. to. .t nov or , .. i_n.t.. q, v1ll be ~ to Un! at. All polDta.

Tbu tor ~1br1_ (aM -Uot ),

• 1 1

(41)

"

h

6.81 H~o! V !l-K~ [*1 7 ( s, , ) J ' 9 TLoD2 5. - sf' (4&)

.... 2 2'1(" d

tl (d/Lo' • """" r-."",' "" • , ..... --r -r.-Eq. (13) 111 plot.t.od ill Pic. (S) and to tacl11"t.e 1.II.Ltcrl Uon U ru.t.<td.

our the ranp oJ: tnt.clroa\ b:r u.. approrlaet. "htl_hip

O.Olm ..

(d/L )2 , (SO)

Slibe Utut.in1 Eq. (SO) into Eq. (l.7) and inteilut1n1 the be.elI profile lInder t.h. equ.Uibrlum coMitan o! 8IIhbllalMd 1IItIUcn beCOII\OII

~ .. !i2.7) J [In (.Ol)JS - .OJ.6.1. d) • "'0 'It' tg

1ba boIlncIal'y concl1.t1on - 1 .•. , the aeaward en~ ot prutU • .,Wlu_ ti.on (d/Lo .. d/Lo """ and J: " 0) _ ...,. be interpreted in 'urioua~,

1. .u a point ot ineipUlrt. • ..u.nt .ouon.

U*r UJ.. a!'1.n.1t.J.oD ot illcipl"'~ .,,,ion, t.b1.l con41Uon ... '1. applJ' ~".r ~ local-- • ..u.ut. Ibe is lar",r Ulan the "1nolpl.,." alae- tor the &1"n local _YI and bM.cb _lope. For a un1tono (co.-tant) .and 81.u NId bHch _lope, t.bu e ..... be \.boQiht. ot :Ill t.el"llll ot depth u picwnod in 1'11' (6). n.. 1n<:lpiet11:. POUlt. 111 shoreward ot u.. equ.ll1br1u. point aDd all m.UJ.c " 'I. .,Uo" .. " be ahol'eWard yield1ll& •• d1g1n&" proru • .

the .:top. v1ll he d.iaoont.~ at. euch polll~ atnca the 1n<:1,te.nt. point. 111 located ~r tb.. U8UlllPti«! tat. on 11 ... navan!. ,ide d/x" ..

('/ .. ) .. dete...wed !rTCI iq. (20) lf1U1 0{ .. 0(. • whUe JIlU t.o u.. 1JICip1ent. II

21

'0

"

.. " ' f­

" I--

"

"H1

"H-I ,0H-I

C .

ZONE OF NO SEDIMENT

MOTION

ZONE OF ONSHORE NET

MOT ION

/ /

/ .A" ' /

"",.CONSTANT D "CONSTANT

tNT OF INCIPIENT MOTION

OINT OF ESTABLISHED MOTION EQUILIBRIUM (NEGLECTING REQUIREMENTS OF INCIPIENT MOTION)

(0) DIGGING PROFILE

C

ZONE OF NO OFFSHORE

MOTION NET MOTION

-+- -1

•

ZONE OF ONSHORE NET

MOTION O<o=CONSTANT D- CONSTANT

OINT OF ESTABLISHED MOTION OC EQUILIBRIUM

OINT OF INCIPIENT MOTION

(b) BUILDING PROFIL E

Neure 1: . otr.!lhoNl 1koIif'.d.a..""Y Condition, rOf'Thec ... uuJ Equ1lih:1"", ProU.lu be· thoo uhllht-oeci "'.otioll Cr:!. teM,m

_bo .... !d. ot t.n. 1ru:1p1e:rt. point. 'tM .lope hu tt..t TaJ.v;. ll'I"" '1U'7 t.o utili!)' the .. t.ahl.lIIhed .. Uon cond.1Uon ot iq. (47).

fbi _ &r~nt. ~ pl"ell1:llUb~ be .pplled t.o hu,,""'. ~..s ot naturfJ. ...-;I.e hArln& • w14e r.n .. ot d..... For ~ pW'JICI" • "pnon"t&th. (COIl8t&nt) ~t&r a1cbt. ~ .. ~. IIJ U'loIO ..-d.al ultl<l, llllId tha "alau.l.tl,j)na earrt.a out til 1nd1et.~ .bon. Larpr 1nac.cunc1 .. are to btl u;pected ~ cour .. UIldtor Ilich .pproxJJoat.l~.

2. .I. •• point. at toqUllib ... t..o .. t.bH .• ~ .,!.1cn &.II vell ... point. ot 1nclpt.n~ .,t-1on .

S\l ch • cond1Uon could .ppl;r uaotl,y onl.7 1f~n Eq •• (~) and C1a 7) ~.ld .~t&n.oud1' the .... .,qu1llbrl.1I.II reUot1onal:t1p t:.tWHII 10.,1l w, .. , lI~nt. and ~aeh dope .... prACIUcal .. Lter , havn.r, both Ippen IWd 8.111 .. .,n (1) ...... ll .. X1l..l.er and Ze1c1.r (6) 1IOt4 U1at t'- NIt. oIl.horll • ..u...nt ,"Uon 111 "I"Y weak Nld of lWt.ed IIXt."t . nw. ttu. l eeond ll'rt. rp .... taUOn 01 the ou.llOrll bo\uJIkry colll11t1ot1 II1lbt ~ ... UHd applicable lIheNo ..... th. 1II<:1p1.ot po1nt tor I chen ,-!!!"""'" and dope 11 .. otlsho ... of the _tAhlliMd .. t1.on equllJ.briUII point. . n. ... tile ••• ward ut.nmlf.7 ot .. Uon 111 d.te~ by htt1n&

(/:. • 0(0 in £q. (47) . Snch .. CIOIId.1t.1on 1 •• llovlIln 1'11. (6). !M '~ U co .... UrmOI18 &od can be , .. n ta Ti.ld • "bu.1l.d1na" pl'OtUe.

B. S..u.-m. Sor1.1n1

1. 1nclp1ent. MoUon

Equ.t-ion (20) NY ba .olqd for u... d..U:JIrl,I!T of aedblent. Juat 1J\ l utle 1Ntlbllit.,. wm.r thI loc:al 'II,,,, and buch slOp' eanMt.iona'

,,( ~) (S2l

in vtU.eb 4' 11 tha ancl. of l"8JID'Il of the beoi-part.ldl .,.t... and baa ba ... ~.­t.eI1l1Md ~t.a.U:r u1d tb.eo .... t1c:1llJo' for .,1rlDU.I rlUoa of p.rUcl.e too bed I'O\I~'. Dill ' b7 !&&lIlon, Our. and 1'w.Mt.lt.a (16).

'or 1 b .. eb of p ... n proflle and ineiAent "'I"', eo.p ...... ..:!. of • poorly Veiled (Vide r.,. nf 111._) laDd, thI "1.neip1ll1lt. lise-, D1• eM be .lIn f'roo:* tq. ($"2) too YIU1' with depth.

2. !st.abu.hacl Mot.i=

!qqat.1.on (1.7) ...". be .01.,.., tar tba di.&noeter at IId1aent. ill o.dlbtinC equ.111bri_, D., under t.t.. l.ec:al ...... u1d be.toeh Ilope conditionll

"

De - [6.81 (53)

lihic.b 13 V1Ll1d only" We're D.<' Df and 1D wh1ch H, ell defined in Eq. ()) u a f'un(;Uon 01 bed-part1~1. geam.tr;y and ha.!I alao -w.en dete...med lIT Eagleacn, Dean tnd Peralta (16).

For a beach oJ iinn prefile tnd incident. Vln'e, c.ompolS!Id of II poorl:T grllc16d .and, the "equ1llbrilUll duo _ De - Can be 'ean !ro1II i'.q. (53) I.e V&ry w1tl1 depth.

"

'nI4I "a" t..nk in .. hich ill o! t.bI U])I'riaanU u. c.rrlild. out is a ~ t..ncuhr &Us' valled chan.wl 10 leet. lonI, 21 1' .. 10 Vide and ) 1' .. t. d"p, le­cat.«! 111 10M !b'drodyn.uIic. t..boruory .10 M.1.1. \I,TU U. ""a.rued .10 on. end b7 a horbont&l.lT rote1pro<:Uuli: paton aetulAd b7 • Jo'd,raulic •• """" MIlh&l'l1n. with cont.inuoull;r Tar1ablA; '11"01 and Itorok •.

Ippen and ltaii:1UCltl (l) pruent. • MIre d.tillild. d.U:cWls1Dn 01' t.bis equip­.nt., 1.nc11l41n& nw.rollll photoU.phI:·

:8. \I.ft KeUUrtlNllt r.qu.ipm!nt.'

The ...... period, T, u ob~ by .... urine wi th an el.ct.rio tJmer the t.iM required (or the ...... "" .. ru1n& paton to compl.te 20 oec1ll.at:ton...

The .. av. h.ili:ht.. of th. 1nc1d<mt .nd ran.elAd waves ... re MUUred by • pt..t1nu. rl.re reIIhtanc. pUI" TIm PIlP, d.veloptd and. lIIIed en.nab.l;r b7 Dean (211), CONlUt.e 01' two parallel pt..t.1mm. v ire" .. ~h 0,008" 1.n cU...."ur , a.t 0.25'" .part.. Th. "ire, .re .. unted DD • tr_ 'D t.hat tha plane o! tM virN 111 perpend1eul&r to the lort8!tlldinl.l ui. 01 the V,Te t.I.lIk and parallel to UI. c .... at.a or the onoo.1ng ",v. t.rain. The denal lroa th6 PIIKfI 1& re­corded by • Sanborn, KodIl 150, racardin, o.oUloiraph. Th ..... P 1&1 eall­bAted IIUUOall,y by ftlTing n up and dot<n with l'N'pect t.o the lUll vatar leTal. Th1a suUo ca.UbraUon hat tIM" proTe<!. TaUd Wla.r ~e condiUolIII b7 oecU­lat.ina: th4 pup .t. di.Uer.nt treqIHll'lc1u with • lalcwn cUsplaclMnt in nUl w.ter.

The ... .,.. puge 1. IIIOUDtec1 on • ult-P"'ptllled carMa.p vMc.h .. T&' alonc t.he top or th . ....... tank on alu.1D.WII raU.. See f'iltllre (7). The .,.,log car-r1ap 111 nee .... ,..,. to obt.a.in the .nvelop' ot au1=l.m .... v. a.plitud.. rrn. th1a v ..... envelope l,.hoo incid8nL and nfleeted "T, ha1~te and ran.etion co­..rtio18'l1t..re oalcul.t.6d .. Ihe.." ill Figure (8).

C, Thco Labor.to7 a. .. gb &lid Sllle"

1. Eqllillbrlu.a:Beacb /"r{)t.llee.

The be.c.b CO!Ul1atl of 3/11~ .... rnublld. !larina plJovcod eh .. t.a IIOrewed to a .tee1 lr ..... It. bl.ll • slope 01 1:60 W is 2.5 I .. t vide bt 40 I"t. 10ns. SW u pl.ced on thta buch with • ~ Udckna .. of II inches .00. s_t.hed to • cheaom unUOnll alope. Th,.... aU1'.rent ,lopls are ueedl naMlJ', 1 on 20, 1 OD JO, md 1 on 4.5. ... .chelllStic diap" .. ot the ohanne1 shCIVinI: the ... r10U11 alope.e 11 IlrNent.«! In Y1IUI'fI (9).

Th ... ncI \III1td In t.bI equllibriua aach proill. e:.cperiJl8llte 1, • vlll eortfld Ott . .. . SWc ... nil (/11 S1lic.) WiLlI • lIND 4i_tOIr 01 0.37 .. and •• p.cific BTu1.t,' ot 2.67 .... u.,.. ~il ot tJw 1.00. 11 pren.nt.8d 1n 1"1CW'ft (lO).

"

Figur~ 7.

Sanborn Ollcillognph Trace

29

'"

I"\gure 10 .

2. SciiMnt Sortinl i'!zperaent.a .

TN pl.7vood beKh ... 0Id in the ~t BOM.1nr; u;periMn~ hu • dope of 1 on 20 and it u .Had. to tha jlua valli or the " , .. t.ank nUl 'VlIterproo! pitt,.

~ d1trel'\ltllt. .aDda Qre ued tor the aedi .... nt. 50rlin, up~1.

-~,

). ... ve.l.l-rolUld.cl, v"U-cnd.cl dUe. sand..

"

J,., Equilibrlu.. Such Prattle Experi!!nt. :

Udnc; •• .:14 a t ..... .r~ unifarll ,ue I.!ld Iln 1nit1All;r phl>l un1J'OrJI 'lopot" ................ propeplAd anta !.he beach IlntU TieU&l. oblern.t1.D ... or ..,cce .. 1 ... prorn, ~U 1J\d.1c:eted en ~equ11ibriwl· oond.1ttaa - t.he t. 1a, t.be bea.:h ~...:I Ln .uentiAll¥ • cOlllunt. polit1«t e> ... r •• veTIl. belu .... at w... The n_ I'IqIUred t.o !'Heh Ul1. aql:Wbriwl pe>IUion ... r:!JId r ..... 121 t.o U2 .. ~.

DoH to ~lee1 lWte'l.ione: or the .... VI chennel. end IIMr1tor, all ..... " •• 1IIiplo1.d .... NO .hal.lC>1f· .... t.er ........ , MOII' .... r, whoIn pe>uible, • et.W .... eUr ~'l.1I ..... _int&1ned of .u1'r1c1.ent. _&n1w.~ to pIlt. t.lle pe>1.nt. e>r incipient. • ..u-nt ..,UllII CItl the beach. The .... ,.. ... leatad ~ to be larp IJlOUIb. to _ tJ> ... "dl -.nt. particle', yet su.U enoush to .Int.t .. r.O.eat.1o,.., EI_ lenUIll,r onlJ" two 411:ru.nt " ..... "I"" undo The charant.ar1AU .. . ot thue v ..... &r'8 u.t.ed in T.ble 1.

ThII t.UU ran oont1.nual.l,J d.q and nicl't. W.VI eher.cUd.tiCI ...... _ni­tored &lid ....n.dion ooatt1c1enta _uured 1Ver, 60r 9 hour.. The period or the ...... v .. .m.eked ....... otten and prond to "UY by onb , bout ! 1 ., The point .t vI11ell the vav. v .., b ... ald.nc; and. the type or bl"Ul:.r ...re e1..l0 1"1. cordacl .. ell Lu. the v."e per1o4 vIS ch61:~.

Buch proro, ~.--u '"'1"1 .-de .... '7 o.S rt., loDCitlld l ... 1l1 .t. the int.erle>r UUn! point.. ot t.ha c:h&mIl , ..... 1nll • point pup ........ neI.d r ..... e~_ tul.l;J l .... led. re.J.lJl. n.. two FOru ...... no then ever-.pd. to obt.a.1a the fint.l protu.. 'the point gaur .... equipped vi th .. photed 1ucdte toot _..urine 1i 1nchll in wldth &rid 1nc1'.es in the direction or1ented rlt.b the beach UtI . The ""VI v" I'N4 to ~be ......... t 0.1 .n,

B. Sed1msr.'I. Sortinl Procedures,

n.. o~ e&lld ... pl. \lied in the experu." t lho\l.ld • I n nU Veded and ha .... un11'e>lYI lnit.1..IJ. a1u -freqltlllQ" d.1atrih\l.t.:1o" e> ... r U. IfIUn bee eh lur!aCI. '1'0 It:c~1U" Ul1I, ill o! t.b • • and 11 e11V'1d IInt.n ezv p ... n du doel ~ aJ\anp ..... Ulan 4S chlrin ll I 2S-tl.Jnlt. period e>" • lIo-1'ep dlTinI ow:b1J'Ie. ThIn Ipec1!1caUons I~ within Asn! ItanduGa (2S). 'i'b..and 11 then thDrou,&hlJ' II1Hd viUl a Hobart mender. A!ter blelld.1ni. the oril1-nll. .u:ple 11 aprlad bT 1onc1t.ud1n.Il lIIc~tI of two tilt (5.0 sqU&rl r_t. ) oa th. plJ'VOOd beach at. I thickl\68S or .pprou-u17 1/11- and .t • Jcaovn dans1t.r (lropprmtiJoatAo17 SO (IrII. / rt2 ) in the !'1r.-.l u;pen-nts . The nnd .1IIp11 11 " ­.woad t.o I"IIIf,j.fl vlll-Ulded throu llhout the 'pr1Iading proc ... .

App....n..tAo17 IYI..,. Ull'M houn the "IU pertod 11 dottAorwiMd and at. t.b •• nd or the e:r;pen-nt. a t.iMe averlged period 1s ce1~l.ted . The va ... l\el&1lt. 11 obt.a1rlld _I..,. daht. hooun u. 1nc tile pll'l.inuIo II1re ... s11t.aac. pup &rid thl S&nhorn Oee1Uogr.ph. "U_ ."er", ".v, lle1111t. 11 Uwa calcul.ted.

"

'tlBLE I I SWf'.ARI OF D.ltA FOR EQtI'ILllIltttlM PROFIlE nPDUMtln'S

un"" t.ot 1 Test 2 Teet) t .. t II

D - .37 .37 .37 .37

'"'. 1 en JO 1 en JO 1 on 20 1. on 45

MAX . llEl'n! !to 1.46 1.62 1.58 I." TO'!' . TIME 01' "i"tS'l' hn 121 167 137 '" , 1I0C. 1.5) 1.15 l.15 1. 5J

"- !to 0.J21 0.2$12 0.301 0.274

'" f<. ,.u. 6.27 6.25 'J.n

K 0.18 0."" 0 .094 0.016

.""""" ' .. n. O.J56 0.)14 0.)25 0.2'J8

r. !to ll." '.n 6.77 ll." 80. 0.02'}7 0.04611 0.0Li66 o.cnll'J

f3 ft . -1 4J6 "3 "3 "" •

cr- ..C.-l 4..10 5.46 5.46 4.10

r.(J .0562 0.1250 0.1))) 0.0404 ..... ED'£RD<M.U.

"'.30 ",,",0

dau;(IHCIPml'l') 45.)8 "'=""" = 6l.U 116.02 52.08

O<m:I!IONl

tiillf~m!BD ~ 51.1.8 uo.6S 35.29 52.81

CRrn:IU<JI )

"

PtorlGd.ieall.1 durilIC the flXpnJ..ent, u.. urd b _thad o;nlt. bT ~"""'iJI& it. perpendieular to the longit""'n,' u:I..I ot the bq.cb. ThU". do_ to 1r1R1'11 that. t.be large: .and pa.rt.iel .. an 1XIt. intcrttlrlnl" V1.th th' • ..naT part1el .. ftieh .....,. be wxt.rn •• th.

The ~ .... ~ to ehoel on tboo baacII IlfttU ill oC tM e..u.l1t ep­pun! to Mno _topped .rtnc or 110 in ollcUbUng equ1llbria. 'I1l.b 1WUall,y req1li:N .bout 120 too 140 hounI. no. exper~t 110 !.hell no~ and t.boI ... t.er dra1zle4 trGD the Dft tallk .

UJ. of the .and 110 eaNtull7 oolledod :I..rI. two toot longitud1naJ. 111",.... MIlt. (S.O equan tNt ) Nld ,.eh suple 1M dried all4 .i..,~. Tt. tinal der\ll1t,' po: IqIlal'Ot toot 11 COIIIpUte4 Nld the n4Ultll art plott.ed all .hOlm 1n 111\11'111 (21), (2~) and (2J).

,.

l. E9':!1l1bn..u. Beac:h !'rotH' Experblenta

1. f'b¥*lc:al Deec:rtp1.1on of bperu..ntal T'lIta.

I . Rippl. Ma11<., Sbort.l7 att ... tha wan, sl.aM.ed .hoal.1.Dc on ti" 1n1.tial..l¥ -.ooth beuh ripple .un torsell. n.q IppeUIId t:l..rllt 1n ... .:y ahall,. WI".r atv.Ull& outwards rr- -u d1.t.urtoane .. in t.tw PDd IN.rhc:a. Trt&&.rlld b)' t.be NI"~ .. u.e r .... _aU ... rl'aoI llTOcuJ.M.Ua. tha ripp1 .. propqat,ed ill bolt! .u.r.c:t1 ...... trOll their point of oripn and Within a rev hours r;raduaUr ap~ad into deeper water untU • llait1na dept.h .... n ac:hed. .It this dllp1.h there 1'&:5 a .uklld 1.ren.l tJc.:I rroa • -.oot.h to • rippled bott.ca. AI no eridtsK:e of Hd1aenl. \..z'1lISp01'1. or c:hanjj;1t .in prorUe c:ould be lIeSft on t.Iwr _t.h bo1.t.ooo, u .. tnnslUon trc.. _th too a rippled bo1.\.011 doa:-lJ' ..... k.-:t u.. potnt. of 11'1Cipient. depth.

Th. local ...... lenr;t.h of the ripple. wu 1.m" ... sely pTOpOM..:Ional t,.o the dept.h -.nd appeared &II stated b,. ear1.1.r 1l,.,ee1.1p1.Ors , p ropo .... tional 1.0 Lb. loc:aJ. qoc:lic: cti$plac:e=ent or • bed par1.lc:le. '111. now sapu.tJon c:aUJIed b7 the rippl.s will aott11')' t..b. , ... 100::11.1 profUe vit.h1.J:l the bo1.t.o:. tOllllda.ry la)'1I1' fro. the l-.1nar OfIe considered 1tJ this 1mtutipl.iQrI . Tbu. this sw<l;)' does not. pr.41c~ the 00::1:\lt't"enc:. or rippl .. nor doe. U i.U.e tru •• ccount or the el'hct. C.u311d by w ir pruane •• S •• 1'l.~""~ (U) .. ><1 (1.2) .

H 1. 11.kely that \.he riWlu willlndllce t1,!t'bulence rlth1n th .. IIoundI..ry ll,)'er and that \.I1e ndilllerlt lIII#pens1on th\I.lI p.-educed 'Illl _od1ty t.h. t.nonaport .echNU_ conddered hardn.

b. ,"onshore Slqp" The !'tTit pU't or tna be.Ch profU. which undant<mt s challia 1'''' U.a1. paM. .. hich l.IIe ... tar IlUrfac e inteneet.lI. It ahanald npldl7 to a neepe.r .lope and "''''''''''alJJ' to • Ilope eeurlnd¥lnyer.sel.,. propor tionsl to ~he ,,",Ye I t eepnesa , I!ofLc . Thh ia ill qr_UlL ... 1U1 Rec t or (ll). The UIO\!I .l.paed t o re.ch the t1.na.l elope ee •• d dllpendel\t on both the irIoid .. t ..... v. o.nd initial alope.

n.. antl. of repoea or the sand und .. w" l.er Wall ...... red 1.0 b. 270 1 hair ..... , the st.eeput foruhore alop. __ nod (eee P':1&\l1'!1 18 ) IOU onl1 about lLo .

c . Modul .. t.1ons, The .ro~ehore elopll Ullepenad I.e 10118 mahT111 "I.~ CI.rr1~ up on the belOh aboy" lJIe 1t.Ul wl.hr 1 . .. 01, This lIand cu. tre. thll 1neoon reel on &lid o.lIud the locaUon c! the br~kal' t.o ",",a turtbr ollllloore before breaking and It. t.he .same tilll ClUSed the br eaker to be ..ol"II of • pl~ type.

"

N.gur 8 n , Photograph of Wavea Over Fe_en

F'iiO=" 12 . PI'Iot.o&rapt nr 'fnI:lcal 11,,, ... ,11 Conl'iguT'llLi on ilt EquUib riUJI

Th. wav. nneet.ion vMeh va, Wt.1.11, -.all CI .. 111=' 1). IIQW ineMiuld WI to the c:cmbin&t.1on oJ thl .t.I~ tOMl.tlo,... and thl onabor. pout.1on of t.hI br ... k..-. tb. lar,1 l'$tl.,;t1on caI .. d .inu,olcial aoduJ..tiClnl iII 10hl bed. .. could bl reuonld froo thl IIIU. U'Maport "tioc1t,. ·OdulatiON! in Eq. LXl). Th ... -oduJ-U.ONl can btl cl.ul,. _ in J'i&!,lres (14) ~ (17). Their 'II'VI l .... th appMrI .. Ml.t UW loul. VItI:' v ... e lqt.h vb1ch 11 a.bo 1n lceorclJnC. vith r.q. C)O) •

d. RetlecLim eo..C!1eierrt.: !hI ...neet.1on cOl1'tic1lnt, fillll'e ( 13) • caD btl nen to lhew , periodic t.andlncy. It hal bun .,-plainld phTUc.uy IIb3' t.his coa!!1C'ient. iocr .. 1d Cro .. it.ll illit1all.y -n ... lul. With th. pl~ on_bon breaklr .hich i. prelant WId.r concl.1t.1on. of lara • ...n.cHon the und is app.arent.ll trllllpgn.1d 1n -uch I wl,1 18 to rW. t.h!l bot.w. cl t.h. s_1.I'd part oJ Ot. inlhon nc.1on . Thi. e ....... Lb. locIUCIfI oJ thol b...u ... to 410""1 n.,ard and thl b reaker to d\arJi:1 to on. ot .. Iller. 1Ip']] illl natu.rl. .uonc with .. ....u. chI.:lCl in the torubo_ slopi t.h:LI graatlJ r.duc .. tt. -..cn1tude of \.he 1'.0. ... -tion and. h_el tbe ~ht of t hl protU. lIIodullUoNl .

'111. SMV&rd apill.1na bre-aku- IIQW t.r.U to aoov. 111 •• and fro. the ..... ard to t.he shorewlrd p-.rt ot the lnahora upon. Th. loeatlon ot the bruit.,. v11l 1,1111 ....... enoreNard. and th. e,.ell b.CinI .,1iD. AI thl profUe reaches aD equillbrlua !.hs bualter t.ends to It.abW.., at I. 'P')]'. breue.T at I. ,.,,,a.nj location and C:OfUl~UIllt.l¥ Vit.h I IIIUll Ntlection.

lMo .... g\:;IIent. etat..d h .... app11 .. tor all \.elt.. and I... lnd .. P!lndent or the inoident 'IIIV' and initial uop •.

nrr .... 4!Jo.naior\ll 1lI.Btll:ll11U." ill the vlve to ... (1.a . Qrolll-

.. lTee) ..... e obetln'sd several t.uu ellpecl~ 1n th. inshQr .... aion. ThQSII .... re dull to 801!111 tBlpOral)' ~d1J=-nI1oMl bottOlll cont1curat10J11 and dull to the.lr trllls1tory nlture .are usu.ed 1l8,11,lble as tar IB the ultiJUlte equU1hriUIII protila .. as COrlOV'DJd.

1.0 \.he 111ht of the preelld.1nl thllOret1c:&l dllcu .. iOl'l (S.c . In) . it. b l'IICo¢zlld t.hat thll thecreticlJ protue or I elJld beech and. the location or U. uavud ut.r8R1ty of it.. profUe lIocI1t1c,Uon by WIYU _1 be detf!nl1nsd from either or the two equWbriUII aediJllent aotJon critllrle.

thQe!l wo sediI.nt IllClUon oharacterilUc •. inclplant. Jlot1on CEq,. L'O) I.lId aqullibratld attahlhhld _tion (r.q. "7) ..... now applied t.a Ulo-diaUlllonal eoiltld bMCh .. in t.M Uborato..,. in on1ar to detenl1ne lfh.1oh er1t.erlon. it eit.he.T. iCfl'ernII Ul. to ... ot the prom •• od1f1ca t1on I.lId "hich criterion ioverruJ Ule location of its ottlbore ut.r~t1.

"

0 .40

0 .30

0.20

" REFLECTION COEffiCIENT

0 ,10

/\ .\ i \/ \

II! I

""':;\\ /\ , \1 r \ / !'Q--~t 'j'\. L-\ / / "

1--1 I I ' " I ..Y / TEST ~'Y a """. -TEST 2

/..-_.

\"'T<

\ •

\ •

\/ " •

oL-~--~~~~--~ __ c--=--______ -r~ 20 040 60 90 100 120 140 160 180 ZOO Z

QflONOLOGICAL TM:. N HC>l.RS.

J'1avr- 13. Ou-onoloa::lea) Variation 1n R.tleetion CosU:h:1enh

'/hen Eq. (20), the ineipi"'~ IIIO U OII el'i'-ftr'iCIn, is applied to predict. WI. eqallibM._ protiles for ~h. ~rat.0r'7 CilndiUona 'IIt.U.1nd the n-.J.t i, ah.\u'd~ steep profU •••

All CIt th. theo"Tetiul proW .. detennned h1 t.biJI crl1.er1on Ph1biud. the .... t.Mp slep •• allboolch it v ... eOQYtm1I11l~ to di.$pbJ' ool)' WO ('IM 1'1,. (15) and. (16) ,

rrc. thi, e"fld.nee the inclpien1. .,tJ,on eM. 'I.erion V&II eonelv.ded ~o be inappll«bl. to Lbll eont.rol of oq.dl1brl.UIII beach profUes e~ all poinu e~t. u the ol!lIIhore liait. of profile 1IOd1!"1eatlan who .... it lIN,t b, rtant b,. de!1nition .

FIlrtbAr d.1,eu"ion ol theor.Uct.l profU •• rlll tI •• 1I b .. .u.....tted to the establ i shed IIOtJon crlterl.on, Eq. (47)'omd lu al~$J'I'I&t.e bCN/ldal')' conditlO1l1.

). D1.c"al1on ot Individ"al futs

a, Tell" No . 1 _ ~r, (JII) , 'I'IIla 1.o!st v.., earried OIIl &L &11

initial &lop. o! 1 ~a ,Xl and "'.a lhe 011lJr t1l1lt. In which profil". " IiIr 6 ...... ured u ill!aren~ ata,n 1n the protUe UIOd!f:1eation; namel:r. at. 49 , 72 , 100 and 121 hcun . The chan,e i n th1l pr ofU e ... Hh tim1l 11 lIhovn in Fl&\1ra t)II~. The 1011& 1I&ve ueed in thia tUt (10 · 11 , 99f~.) caU1!led a lu,. raOeet10n co"U~clent which fluctuated consIderably All uen in Filll" (13) •

!tI. equilibrium point lies on:lhora Qf t h .. Inclplomt point in Twn IIWIbJr 1 . '!'he.rer o .. , l 'roill the previO\l' UI!cu"I!ion . lh. "",ward v:~,...-IIlty ct the theoretical BqllillbriUII prom, i. at the ..... llibMUII pein~ IUId lh. "rolU. takll the ehape of a building beach. '!'h ...... II! ntI diaccn-titl!,l.U,. b .. ~w ... I'l the theo.r .. tJeaJ fll'Cf U .. IUI<I the or igin&1 lI .. ach dcp'o

In this test til .. po1n~ of ini 1,11.1 nd!. .. n~ _t1~ did !'lOt fall on th .. cr1&1nal bNch .Ilope es lh .. nuid fore"I! v.n ~. lIrloll(b to .... v. all U)e II!d1a~t. ,:I l ea at t.he ~g .. of tha Uper1ae.nt.aJ beao:.h. Yor this rvuon the only !>wOOlry eondltJol'l wh:lch CIl! t.e 1pJ)l1ed toe I':quaUonU,7} tor COIJ>&T1l1on "1lh the 1,borlto17 prollh 11 tJ\It th .. theor,,~icll IrId ~ri.romt.ll. prolllil ,,'nt I!IIIl.<:h It th. toll of the uperl,..".,taJ b .. ch .

b. fMt He. 2 - Fieur' (lS): In tilt. le.t. In Jnitll.l .... eIl alop. ot 1 "" JO " ........ oId \11 th • ...n.r incld .. , 1I.v. . (LQ - 6.77 n.). IN. t.o the abort "alii lqth the l'flflecUon eoelUeient.a rieur. (U). " fire &flnerallJ' -U.

At.nn Lb. eqo;a1l1brl .... point. 11 .. onsI'.ore of the l.ncip.1ent. point. ill 'rUt l'IUIIbv- 2 and tJnu, tho equ.ll1brt\lll point. tecao. .. the Ie-arc!. P;,trllllit7 of till thoaoreUcel profU.. Th' ow.oreu.cal protU. tak .. \.he shape ol ... truJ.ld:1.n& b ... ch and there 11 no 41l1cQ/lUnD1t7 bew _ t.b. theor.tieal proW. and the orl&1nal beach al<lpl. See~"' (15) •

..

• o

C(P TH

" ,. «........, [~TlO[" <TV <:I I"lClIUI>rM. """"'l-!' ... ~, ,., .. • ,'612"'"

, "

---~ , ... -.. ---- j · 1'2 ..... -_._ •••• - • • 10() __

'·111 __ , ..... ,

" 1I 1 S'A~CE . X, I~ fEET

Test "" _ 1. Buch P'rctlln

,.,., ':~::~!:: ..... ~ ,.,,, ....... "_0'2'11 1 _' 5U ... ... to4" ..........

' ....... , .. ' .... ·Cl 3~ . " 1 • • ' H", ... . " n ',

~ -

•

I 10 ,

,_ .... , .... "" I ............ ' .. . .. "'---,

._- /1

"" . _ .......... . __ "'_"'.0'0)'_ -' ."., --_ ..... -......... ,

_~)~~=;~~ ._ ........... """"LO_._ '," ., ... " ...• ''''

•

• N

1-----------------------------------------------<I----',,'-------1:=:=: .. =: ... ===':=· .... ===:=:=:;; o •

DEPTH

IN

10

eM, 20

>0

o

TI1£ORETlCAL PROfiLE I~~ENT MOTICH

CRITERION

5

T'HEORET1GAL PROFlU ESlA8l,.IStlEO lIIOTIOfI

CM'£RIOt<I

r lMtlL BEACH SI.IIFAtE: (_Ihe~1

~OOI FIG ATION

10 " OISTANCE . X, IN FEET

TEST l

101<>1 11m •• I~T nourt MeG~ Stdlm.nl 010"",,,,.0 - 0 )1..."

II'It~nr wo~. [""ivoltnl Otop Watt' wa •• "-0.301 11 HkI' 0.325 h T ·t llluc L·&.11:3f1, d· '18 0"",

20

Tes~ No. J, ?e.~h rrort:~s

• DEPTH 10

" CM. ro

-, o , "

• ._ BL ______ _ ~= .... . -,,,, .-

fiNAL .UC~

$\HIrACf I .........

O~1GIUL IE""~ IQfi .a \,.0 ... )

TUt 4 '0"" ' ,.,.,.'2U ....... M,,, .. "I .... ' D_*, ~ . O )1 _

I

d !

_ .,_ t. •• _O .. a .... • .. _

H· O!'?4 tl " .. Ot .. " l'I~~oot '.-'MM< L't1311 ".'l"" ,."" .....

I~ to til ., DISTANCE. X,IN reEl

Yen No.4 , aeach ProfS , ,,.

the ".v •• Wlltod in tJlia teet. 1Iert! nat. -rIicient to IIDY. all of W. ,ed1a.nt n~ on t.he bueh and Ums &1\ .xper1aent.a.l point oC i.D.1 u-.l Itod1JaVit lIIOt.lon II ... observed. ThU u:par1afmW 1nc.ipiom'l. ~t. 1.1ee cttlbor . of Ute 'l.heoreUee.l equilibrium point but. OlUIhore of l.he th.ore­tics.) itlc:1pient point. end cU..Cfer. fral th_ by h .6% .m J . ~ reltpec:'I.1v.ly in dtopth.

Th. th80reticel Inc:1p1ent. point. aDd equUibr1U11 point are calCl,l­let«!. uaiIIc the .NII •• d:1 .... t d.1 .... ler IlhU. tbe ~eri&ent.&l.. point of 1tI1t1al sediment III(lUon occurs wher ... the mal.lut particle In u.... .. nd et.IrU to _TIl . Thi. upla1ne in pU't. Uie v&riet.1on b ... tveen the th6GreUc&l aM ~.rt.."t.&l renlt3 .

c. Tnt Mo. J - n.prr. (16): In thit teet an inc:1dftDt. " ... oC Lo ~ 6.11 Ct . II.., 1I11od v1t.h .. .!!It""Per 1n1Ual elope of 1 on 20 . Th. reflec1.1on eo.rCic:1enu were eWlar to tholle ot 1'e1lt. <' .

Thil telt 1~ .'.'1.r to the f irst tllO t •• t. In that. the equilibri um point U.s Oru!.hore oC the incipIent point . Uso, l..1.kII Test DUmber <' , tM uperiaent.&l point. of 1n1t.1-.l sttl.l.1l!lellt .,1.1011 Ues ott sbara oC the theortoUcal ~1l .. 11;1t1._ polnt but orumor e of the I..heoretical 1nc:ipient point and dUf&rs rn. th .. by 20 .0% &ad 6.U reapect1,.~ in doIptb ..

d. Tellt No. II - NFl!! (l"r) " In t.b.1. Len the IIild Slop., 1 on liS , and the long .. eve, I.e. ~ 1l.99 Ct . , produced ,re. t. ,.a.r1aUons in \.he r.Oect.1on coe!tici"'lt. The periodic t.eruil!lllCY or this codflcient. 18 obeenod in figur e (13) .. The t.iMe to reach 'PIIe ' ''ent equilibrlua .. <'<'<' houre , Ilea 10l\ier Ulan 1n th. oUler teste bec:au-" the bru.kar locat.i(ln did not ,t..&bll:h<t within the a.l..JIoat cOnllt.ant.-dept.h 1nabore region .

Thie t. .. t 1. the cnlr one oC th<t UJl'f'Tiaentll 10 IIhlch Wle incipi . nt point H .. onshon or t.b. equillbl'1..llll point. flO"II .... r. th. dUrsr.ne. between t.N. 111 cpdt. _11 .. eeen in FiJUTe ( 11)" Therefore, \.he l.heoreucs.) pro!11e bec1na .t. the inc1pIM l. point. IIld t.ak .. t.be abepe of • n.l. d.111ini Hach . Sinc. \.h. 1nclpient lind t..h, equ.:U1bri..- point lITe ~eTY clollS tC/icther Lh" nett.er lIilep. of the t.heoretIc&l prorlle 11 not v<tr}' ... ia ... t. .

~ onllbon nvid Cor ee.!! in t hill t"a~ liar, l.a.rl" enough to .a,.. all 01' Wle aedaent on the bM-ch and no expU'UlenUl Lnc:1pient point v •• ohe,ned .. Thue,'" in Tea;' No . 1 , t.he boundary condi t.1o.., of Equetion (141) requj..rn _tchizIj: or tbeonticel lind uperiJlenTAJ. prof U.e s at. t.h. t.oe of loh" experlavlt.al b .. ch .. .. ......."

Th" bellch profUe experiment a 1ndic.l.. that itl , lIInarlll t h<t Lheoret.'elll proCUe ;rr$d.1cta .lopu t.hllt are t oo ,te<tp a t an:r given

dr!plh , d • k, ror. Cb .... d J r.

in wbieh UI. par.etar It il dir-eet.l.y pl'OpOr wna1 to t.he IltI...,th ...... t.ransport veloeU,..Ot. Ther-e!ono it k 1a redueed, Ole slop., a<. , will h redueed . Th. steep t.hecret.ie-.l slopes thus ind1eata that perhepl the .... ,. t.ranaport vel-cd. un predict.ed b,- loh. thac,.,. srs l.arcar Ulan Uo.oss which utllally occur.

e..anold (lJ) poiDtl OIlt that II r~ed nrClclI CIUJIS • lolal reduc lolot 1lI thll Co."Yard IIII.U trlllleport nllAr t.htt b~. equ.llibri_ buch profile lUperialll'l.ts ripples were Cor=ed..

• SIIbet.an-In all 01' the

The loIIIOl>I'It that to':l. theoretical IlAU transport 1'aloe1lo,. 1III.t b. redue~ in ora.:- to live qJantit.ative Ilcpe pr ad1ctiOll Cllll be CalCll. lIttld b,. ca:r:pu:lni: the theoretical alopa vith th. l!7pw1manW .lope at. an,- deploh . nil redlletiar: 1.11 ... us t.r.nsport nllell8 ... ...,. 1a 20S to 40:1 .

As noted 1n the rllView o! previous work SeY'ral !nYHUS.ton ha .... oll •• Uied h .. eh"a aecordinc to th. magni Wde of the il:Ic:ldant de"P"' .... ter w ..... Itlepns.II, flo. \/hen Ilo .( 0.025 • ..at.ar1al it .. id to bs carried

t;; t;; in the onllnorn d:1rioetJ.on naltaning out the ott·al!on racton and b\l.1.lJ1. Ul& up the region neu and hqond the breaker. ConYer-lIel,., wno with Ho > 0.025 are said to .at'e ..... terlal in the offahore dincUon .. etrlpp!.n& tho IIInd from tJI. breakllr rtCion an4 depod tine 1 t in thll oCf3hore region. lharetOl'fl U", o1'1'ahore region bUild$ when Ho ') 0 .025 and L t n. ll.a.'UI Io'Mn Lo H., <. 0.025 • ..

11le building !UK! nalt.enirl, of thll ofhhonll region as a function of t.hll dllep- llater lflIVIl BteepnllSf. 110 , can nail b, corrtp.nld Vith the

t;; Nllat.ionehip found hllre1I1 bet:.1e<!n ~he location 01' tha !ncjp1ent sad thll equWbri .... point . .I.e not-ad pre'riQllsly. 1.r the incipient point ill offshore of the eqIlliibrlum point the o1'fsbor, RPon \nIUda up but 11' the inCipient po1.Dt U anshtlre Ct! tilII eqIl11ibri\ll'l point' naher digCi", profile relNlts.

te lllat n~ers 1, 2 . and J. tba inelphnt. point wll8 ottabor. 01' the equ.U1brilllll point. which indic.t. ... a bu1.ld1n& beach ville in Telt. lUllber L the indp1.ent. point 1a oMbon or the 1IqIl1l1briUII polnt whid!. lnd1eat.as a dig&ing, flat~ profUe. ec.p&r1.ng LIIesll relflll t.II wi th the -.pllr~eDtal W&l'e ateepnfl55 ratios 1ndjcat!4 conaiat!Dt IIrlOEant. with

• •

T~"l No.

J

,

J

,

PRFIlICTIotI OF Cl!A.llACTER OF THE EQUII.lBJi:IOM BEAll{ I'ROf'ILE IN THE 0lFSHCI!E ZOI/E

Deep-Water Incident Wave Steepnallll

Hio/Lc

orr~hore Beach CharactBr AI> Given By: &{lib.cil R(Jt; 'theory PTe~entid Ei'Per'LMnL

Criterion or Hen (Fig . 6) John~on(9)

0 .0297 BUILDING mIDm, .DIGGING

0 .0461. &lUDINO

JIIllDJJro BUIDJI""

l.. ea.:parlSnrI of ~el'~ Dau lIT ..... teblng Ute eq>er1aellw equUlbrl_ proJ'il .. at. Ute int.eraec-

1.100 or toM sUll water 1",111 and !.he equ.1llbriUII b .... ch. 1J:t~t.U1a oballl'VlltlODZ1 ean be N.dl!. (See F1a:. 18.)

One of t):e bellie u~t.1o.,. 111 c1erh'at1on o! the lqUatlon o! equ.Uibrl_ prc.filea CLt. l.1} 111 that !.he tono or !.he C1naJ o((,hore pro!:Ue 111 1IIdepend«l.t ot the iNtial slope, c< o' 'DIe 1ocat.101'1 of the proN.le.1!. tied <loom, bo..-.... er. b)' a bOWldary eond.1Uon tn\'ol'Qnc .,(, o. 1(0 conelusicn U: dr"avn nUl respect. to OW t1naJ. pl'o1'1.le ill tbe bnsakl!l' 1'II!1.'ion. By comp.u-inc teats s:plO)'inc 1'1 .... 11 the .&IIe iDc.1c1Gr.~ "all. :'enc!.h and ...... e lIl.eepneN 1:0.11. ditt.I''''~ WUel .lopea (rellt.lI ~ and 3 . '!ItZIt.to 1. and I.) 1t ill eoncludeci thet. tbe !in&l profile, 1! it. ~ 111 lin equllibri_ profUe 111 the oUebol'e r-ea1on, 111 depllDdent upon t.he 1n1Ual elope . In t.be tu..k ... repon Ute tOii'r telt.a almost co1J>cid-o!! 1nd:ic.t.inC that. &1\ tqtdllbrilllll profile .siat.. 1n thb rellion and seems iLldeptmdeut. !)f: t.he ... "". p ...... et.e.r. lIS well •• th. In1t.hl -.lop .. O\'Il>" th" range t.utO!Cl.

The !1nIJ. fonahan dope. &re elJIoat: the 11_ in . ll t.IISu vtVl II al1&ht t.1!Dd«ncy towards at."epIIl' dopeg tor low.r "IIV, .t.e0!J'l'le ••••• 'Itt. nlll".,. roreahon ~lope h about. l~ .

TllII ooncllolsianll dn.vn .trcn t.h •• bove .t..t.lllllln1.& ...... (ollowa t

•. A IIOlIerning fat: tor in Lh ... foran1on or bAch ptot11e. 111 theo bruker. 1t.s eUect tends I.e OVllI' - shadcv other tIIechan1 ... tn tOnUnll an eqv.ll:ibriUII pro!U. in t.he inahora ._ and fa m i-"""'rt.&nt .tacl.el' ov ... 1I\lch ot !.hat part. ot t.he ottohare &00II in whicb IIJ1Y pl'Ot1.le tIIOd:lficat.ion occu.rn.

b. A s""end governing tector in protile ConuUon b \.he 1IZIIOUfIt. of I!:lI<I.1.ment. vh:I.clt can POI~1bl.1 be tl'lInIIpOl't.ed. OIIt ot or tn1.o thl!: 1nehorl!: ap:1 otfllhore rqion. . 11'01' I gillen " ...... and nand th1.a 1_ I' .. lated. !;o the in:I.t1a.l elope .

~. A.tt.e:r the break .... region .torms an equillbrium pl'Otue, the protile in the oteahore repon t onu aolily fro. 1.oca) .ed.1-men~ t.ranllport.ed b7 Ule orbl tal forcel and not tre- led1aent svapt. otflhor" tollov1n& 1ntrtJ.r.ent. b7 Uil bree.lt:er . Tl'Ilre­fori. oft,hore equ1llbr1U11 will be rHdted very lIl.owl,y.

"

..

DEPTH IN

eM.

" .. DISTANCE IN rEEf

===:lUf .. H.JI.. • • O'OSO,II .. loOl

TOT t, II. fL,' 0.0-41,11 ... .to I

- 1[Sf .s, H./L •• O-04I.I .... 20) " TtST ..... 'l" .Q.02$ ,II ... . 51

• • • •

B. Sftdimlmt &l'1.1nl! E:!pel'UlfIIlU

1 . TbaoroUcal Serun,: At a gI: ... n oUabor. po.ition (1.a. at. a kncnI:a depth , d) 1m a

plano beach cmpo, .. d of a "A.!IjffI of land .hlll, a c.-t.ai.D a1&a pv>­Ucle 1.a Jut c.pable of _t.1on and 11 do!1ned as U\a lnc1911111t. die, D!.. n.." at. U\e .U18 depth anoUuu- ala. parUclAo 11 In otIc1ll.aUnc eq:l1l1br1.WII and 111 da1'inlld .. tha aqu1llbr1.w. a1&a. De. 'lba ,bee, Os. and 0.. CWI b. obtUnad '0,. aolY1n, EquaUOn.l (52) &nd (5) ~apacthal.1 uatn, ta local wave and beach paramet.ara .

'l'he or11!1n&l beuh laDd 11 ua~ to h .... .an 1111 Ual ahe f'requomC1' futrtbl1Uon U oMvn i ." !'iglU'N (19) .nd (20) . Ut.or waT ... at.tack tho boao::h fClr a nlllllbm- fd hOUl"a the beaeh reach",", lUI equ1.l1brilllll podUon and tho ori&1n&l dco treqwlnllJ' diat.rlbuUon changes at. .. ch point. &loClS the b.ach. "Ibt final ahapo Clf u.. loclll ai"e .troquency dJ.atrlbu t1on CmoTe 11 I funcUIII'! o.r Ow local ratio De .

'" U De < 1 the f1n&l th&o ... Ucal. ahe mquenllJ' c11.atdbuUClQ

'" at a given oUahon podUon conta1na taro eplk .. (bi ~lIIOdal ) ... hown in FigtU"e (19) . '!he ap1ke ill the u.all. pVtJ.clo ailO r.ange con-lIi .. 1.8 of the parUclae in CIIlcUlaUnc equil1br-iu. 'I'h1a IpUe occW"a becaWla parUclel amaller than the equ1l1bri\lll ahe IDCIve to"o'ard the br eeker whil!l larler part.iclell l1l<I'1'. i n the ottahor. dir.o!J.on .

The aee4l\d apik. c>c~u:r. bec.uo~ tha il'Ult&ntanaoWl nu1d forcel .... 11U11l,!1"1c1ent. to .... '1'. part.1c1ea l.arS&r thul a cm-tatn .h • •

11' D. ') 1 the final theor.tical ah. t'requ.ncy d11t~ibut1on

'" conta1na on. diacont.1nuit.y u aholin In Plgure ( 20) . ParUcl.,. larpr than the lne1p1ant .b. particlo will l"UI&1n ataUonary while .... ll.r particl.e IIKJVO tow&:"d t.he br .. ak .... .

In Figur" (n) , {22) , and ( 2) tJI .. thso"Ucal i ncipient al ... . Dl' and tho th.oret.1cal equ1libriWl! ahe , D. , .... """'Pared .. a tWlC­t.ion of beach poaition or depth. Both liaea beoolll PMlgrOllai".q larl:flr trOll t,),e to. at the beach to th .. b"u.. . Thue.and beach .. Ihol>l.d bec(KTI' progres.1Toly CO&r1!l"r 1.n the onahor. direction and thia ehol>l.d be evident in Ule alCpftrimMlte 1n aovftral w&y$ •

• ) I.! lI .... eral f1nal ahe troq\IeJICl)" ditwi'out.1one from the off· ahor<3 "'(ion are COIIpared U!eJr peak •• houl4 abUt in the d.1.rect1on of 1ncreuin& . ... 11 Met 11te III tbrlr I&q:IUng pol1 Uon .. &:"i83 !NIII W toe or tha beach toward tho break ....

"

EQUILIBRIUM MOTION

PARTICLE SIZE~_

PARTICLES GO

OFFSHORE

NO

MOTION

FREQUENCY CURVE

SEDIMENT SIZE

Yip;\lT. 19 . 'nlllo .... Uul So.r!"in& for Incipient. Sin tarc.1iOr lban t.h~ Equll.1brl".. Sh~ aL • Giver, Bea.;h roel1.1on

..ilL> I D,

INCIPIENT MOTION PARTICLE SIZE

PARTlCLES GO TO REAKE

/

I I I

/

ORIGINAL SIZE FREQUENCY DISTRIBUTION CURVE

NO PARTICLE MOTION

EQUILIBRIUM MOTION PARTICLE SIZE

L.ARGE SMALL SEDIMENT SIZE

!"igor" ;(J. 1'heoreUea] Sort.1r\1: to r lneipianL 511;'1 Srr:aller Lhan the F.qu1l1br1U11 She .t. • Giv"'n Be.ch POlIjl1on

50

b) A eo.puillon oJ llleaJ1 aMliAent. cU.e t el' With budl posiUon • • hould 1nd1c;ste an 1.n<:T8&11. on Ow nd1asnt. UI. in the OIIIIbclre direc­......

It is al~o r ... .sonabls to e.;pect Ula deeree of ,.ha ..,rt1ng to YIll'Y with depUl . OeolOlht., 4aN.ns III nil eortad lediJo..,t u one '11th. Yery DI'Ill spred of ahes, a ,,_on d.etin1t.lon of thl dllf" of 'nTl.1n( \.001"1 D. S • • '"eo . p~ 111 wll1eh '"50 and P20 Irs 50 an 20 pen::entJ.lo dl .. I"Hpoctivell (!'(Ill • wlDu.ht.:he d ..... fraqu8llCT aut-n. bv.t.1on.

Killer and Zeigler (6) have ud" this coefficient irnlepend.8nt of' Bhaol'uh a1.o b:r divldilli b, ths P50 lilli , 1..,:

D.S •• Plio - Pzo

'''' (Sb )

It 10 ~I~onable 1.0 upect. D.S . as rhen b:r!q . (511) to deer_III 10 the urlIIIl'x>r .. ~Uon. Hore partlelu .... IJIIbjeot to aor t.ing ."t.iGn when ~ near - bottc.. f bld tore .. ~ ""' ............ a t..We decreu1n£ \.hili INIIIlllntor)end '"SO ahoW.d lnc.nua 1n thl onehol'l

di.re<:Uon.

In _ry tile expect.ed up ... 1JII.nUl re.-ulte .... :

I) She frequem:1 ,1htrUx!t.10n crurvelll 1I1t.h aod&l eiUIII (peak .. ) cof.nc1d1 .... with tJle equ1Ubri"" end loelplent .. da.nt. diU.

bl .u. 1nd.1eeUon of en incr .. ". 10 the .. an l..tiaIent. rise in \.be onaho,.. d1rec:t.ion.

0) SDrUnc; 1a: upeet.ed t.o ine ..... , 1.1:1 l.J:Ie ehoreward direotJ.BIl. 1'b:I." will be 1od1c"ted b7 " decreue 1D U.s coat!tcieot D.S. of Eq. (5I.i) •

J. "trruin ...ount ot ~t.&l deY1"Uon frooa I.hh .odJ=l 1:1 e>:peet.td due to UioI folloodna:

.) 'nIe eqveUona ot .. d"-\II'II. lIOt.ton ~ tqL (52) end (5'3), "en dJlr iYed tor III sphariuJ. par1.1cle ntClaeUrc \.lie enrul.n.1.T of th' II&:wI ........

b ) J. een.ein aJq>eC\.ed . Th&t. 1., Plld gra111111 .

• MOUnt. of 1nt-ertuene. blt'llMll the ,and ,nilll 11 the larg.lI· ,and iV~na "'I\)' hoJd down or 'l.rap -..u.r

"

c) h DOt.ed in :M"t.ion n. aut.bor1Ua. ht.". oblU"lad t.hllt. the .. """t. or ofr.hoTl .ed1&eDt IIOUoa. it. "wHIt" and 11 Ie .. :l!t.II exp.ec:hod t.heoreUct.lly. This v et..k otfahore JICIt.lon will cau •• I d ... tUlon f ro. th. rinal \.ht.Ol".u"t,l t.1.e treq,lt.nq diJft.ribution . When Ue 0(, 1 only I

Ill: t.llcht. cl1p bet.wee! th. eq,,1l1bri_ t.nd u.. incipient. ti l " Will 0<:C\ll'

int.t.ud r4 t.he theoret.1ct.lly prMi"t.ed. I~ at. shown in l"1(\1re (19)

2 . !lq>tuJ..eut..t.l. Son.1n£

A total or richt. nma were -..de. .l COO""'t.. ,t.IId t.nd • brick .crt.ar und we:-e used in tbl first tin nmt.. St.nd wu d.iat.r1bot.ec:I W'i'U" t<I the approlit1Q,tff dl!IlUIHy of 2'$0 p.t./ft2 • S1n • .-l,..rt. of offt.b.u·ft sap:!. '"""Ph" tak., t.!ter man,y houre of 'WIV. aeLlon ahowed litU. deviation rl'Clll t.M .... -.d. at th" )loIIK1nn1J'!& of the e:q:>lIl"iIfIt.Ilt . Ttl" •• n"Sat.in rMUlu art. believed to be caused by int.uflU'll'ICff or t.he \op nod l.Ky ...... witll tho>:l. undem .. th . 'nil " . .... s in th .. of!ahore ng10n 1n!lunce tmly t.h. I.Qp .. t.Il.:! Vain l.,.ers l cOIUlequ.ently ~ 11111 ••• th .. toW "1IIIlplt. tJlicknen i.e qu! t.ff ...all an,y .. ~ .. t aor t.1ni 111 th. Lop la,yer. 11 1JIiparcepUblff !'roll • .!I1ev .. t.nalyah.

Th .... !irlllt tl .... nullII indi".ted Uta neeanUy ot unnS tn, follaldll4l experl.Jrllllltal t .. chniquea :

.) Th .. ansu1t.rl t,. of th ... t.nd art.1n. " .. reduCed by urina .. rounded .UJct. (ottawa) slllllli in KIM Btx thToIlgb light.

b) To 'C~IV" aeasurabl. d1!r~nce. in alle-di.t.r1but10n due to wav ... 1notuced lIort11'\i U,e at.nd wdsht " u rld\lced to 50 11'' '' per squt.re 1'00t. .

i ) "... onshore ne&:r·bot.~ va!oc:iUes ""n lncreaaOld by u.a1t1& a 10lll!l.r vave.

Th. Tllte of oort1n& i' a ··n",· at tba beK1<n1nl: 01' t.ha .,..,. For 4IpProti.at.tflly 10 reet up and down Ira. th" breu..r the b .. ch quickJ,y b svept clio'" and. tAh HI1d acClllllll.t .. und.r th .. b:-eul.r eDd a" th. l.1odt. C.r vt.V" awuh. Th .. creat .. ,st cllt.rll[ .. 111 sile di,trlbution wet. pl..c •• t. thes. t vo .... g1on1 a" tIho'IIn by u.. Incre .... 111 __ ~t4Ir 111 naure (21. ) . In Sell"riLl t.he tine. ace!JlllUlat.. at t.bt. .lId of the puh whJ.l. Ut .. "c.e.rs ... IYter1.t.l. t.re loc:at.ed at. t.h .. hrMker. Pen-ahe 1'1n .... 1.t t.lQ'. an W .. n up !II tIUSJ)OIl:lI1on and curied ofrabore near -.1d-depth by !.h, ofrehor.. lIOIoIe lrt.r.aport ... eloc:lt.1".. H .. ,,<:mU'. u.. ...aunt ot f 1J\es loat 11 c:ona1dered to be 1JIa:1&!!i!iCt.llt.

52

SAN 0 PARTICLE IN INCHES ,~ 2J. , .. ", •. 1'''011 ot f'jn&l 8S .. f'TeqoICIC) J}i~r1""Uon

..lUI In:tp1.ea\. (Ii,) ar..d BquUUrillIo ([',) SiIl_. ~or 'rut Ito. 6

"

SAND PAR:TICIL~ IN INCHES P'1~ 2:>. c..p.r.laOP of I"1nal S1u FrfOqUtnc:r il:hLrib+10f1

"ith 1tt'p1en~ CU1) and F.q1IilJ.tr1U11 (D ) 511.". for "Ut "0. 7 "

F1£'1" n. Cclt:pari,O!'I or F1r...:l She 1'rtoq1l.t!v;' D1"rJht10f'1 nth !ncl]rl4!J>t. (D1) 1M Equ1Ul:rb= (D.) 511U [Dr tnt Xc, 8

"

Ripples did not. roI'll! durtn& UiJ at the 8XpU'iJllentll Il3 the layer of sand vas too thln .

III each of tha last thl-lle runs an a .. r~ ot ns, (rauChlY 0.01 UIIIILI p.r w ..... per1.od) of the oripnal lIand nil 101lt. during tbe COW"se or the apel'1.Mnt . Tbt lo .. es t«lk pl.ac:e ..... n thQU&h the pl,-.ood beacl1 WII, c~ seal.-.d to the clus walls or the wa .... tank. The a:a,1or1t.7 of \.helle loaa ... war. ob.enred to occur d1neUy undU' the breakllr and were thUs uw..c! to be •• llttl. dtect IIpOJI the eqnilibrlum aill!!-­dilt.rlbu.t1on 1n W.e oCtabore ,one.

The 1111 Ual an(l tinel Ii'. dU:.rUrutlOlls of the ent.L""fI sand slII!iple ""'II ehown for RUM 6,1 an(! 8 in Fig . (25') . Il ean t:. seen tn.t 11111 louel n. 1IOt> l1a!1ted to the !'iner fracUons 1.11 might be ~I!(:tlld . 'nte appuen1. ~ga1n" 11\ tHqueney of thll II1ddl. shu du.r1ng !tun No . 7 il .. rNUl t at 1i .... 111& inaCCllr .. c1ll1f which &$_ a eons1dortille impor­tanc:e when lIork1lli 1f1t.h .ueh .all quanUUa".

Thll final ahll f'req\leney di.t.rtbuUon eun .. for ItuJl .... 6 , P'1cur- (21) , g ...... raeuJta _1. e~1a~t with the t.heo", . ThU'. an two dist.inct pub at. 0.0059" and O. 0232". '!'he ahe. ber.ween 0 .O1l7" and 0 . 005'9" ~ eona:1df,rlld to be in osc1.ll .. t1Di equ1l.1brl.lGl in the aUahore son. whlle the a:!.uII between 0 .0069· and 0 .0232· are the i.ncipll11lt IIbe part.:!.olee tar Oe/Di<. l.

Thll liUperu.,aslld plot or b"ach position ... incipient and IIquUlbr:!.\I,IIl Ii.., in rleUrll ( 21) lndicatoa tha~ OejD1< 1 f or X <. It. ft., where x :1.1 tlIe d..iatano. elq the beach mU.lIured rna the bellcb toe. Theratore. the final siu frequency dietr1hution lhould contllin two peW :In the oft,lh(,rtI repen,x <.. 14 ft.

In~. (21) , at a typical lIf1cUon, :It ~ 7 tt.,1.hfl theoret.ical Da· 0.0]06" and Oi • 0.016)". the final du fr.quency dist:-1butiOll .t X. 1rl..tiY'. the uper1aent.al 0..·0.00)9" lind D1 ·0.0229". thi. represents a d1.U .... nc. of 411" &nil 29:' rupecUvely.

In iun.e no. 7 and 8 (11,. 22 and 2) 1 l1Ie .eand ahe J.nt.U1'al.e ware halved by doubllD' "he maher of .ievu employed in the mu,.ah. In Lhase t va runa thero were dletJ.ru::t. pll&l<l in the tina]. d ze .trequ.ncy dinrlb1.1L1on eur-vu. however , the peal<a did nct aMft in tIlfl cli.rt!ction of increased aedjll'uw.t du. Near the toe of lJIa b8llch thn theoreU"a] ~i"lI, Da and W , coincided with t vo peakll in the final Gi u trequll!!lC)' d1ltributial plot. .

Parlwpe the JPOe't notahle ob'er .... Uon to be _d. [I'0I'l Fica. (21) J {22} and (2)) 1.11 t.bat the ,r •• teat o:haqa in aha diatrlbuUoo. occurs IdUl the lar,er .i.t.... . .Ill all U\MM TWIll the l.e:rter lin-. deere"'e in frequency u the hreak.T 18 IIlPl'OI-Ched . Tb1a is explainable ~ Lhe

t.hftOrY present.ed only U De « 1 anel 11 t.ho .ctlla! D:1 1. u large &!I

!5I or larau than th .. ~ eHe in the sample . In iJUch • cue Ole" larger' siles woul d :!lOve ofhho ... (See na. 19) but. line. no Inc ..... " in the CnqueDC'Y of lars" .1&"8 wu obeer.,.d TIe&!'" the b-.eh toe this "z:plMllt.1~ 11 1;01. accept.abb.

Same .ec~, I1hq t.he breaker intluence, 1a .. 1dant.lJ gp ..... tUIC lIhlen 1.s not 1m::loded in the theory .

ll\ P'1gure (2l.i) ~h. _an di_t..r and sort.1ne co,Ctic1mU are cc.pared with bef,ch po8it.1on .

Hote that ne-ar t.he beach to. (1.e . up t.o Il>out 10 teet) the lIIean eeclitltmt di ..... ter dou 1nO::l'Sue "ith diel.anC:a 1J\ th. on.shont d:lree­Uon all pred1cl.4d but. onl;r sl1&hU,. . !he luS.at ~UII beinB mout .m bet><een 5rt and II ft in Run no. 6. •

11'1 bcitvllen 10 n. UId the .lrU$pend all bu to the

'~;~~~::~~-; lillian diUleter und..r C the llean _evhat in the adjacent

=u.s on both :dde. vbere eII'llmcied •• t. ... 1-.l. are de'p<lehed.

l IIIICOnd and actually JOOn ilIIportant. reason Cor the local deer$&lIe in Man d;1 ...... tllr I.IJ WI. b r eaker 111 approached 11 the deereue in the frequent)' or th" l&rler stu. as was not.ed "0118.

rn !!:una no. 6 and i the .orting: coe!'!1eiomt. d.areued in t.h. oUmol"Ol :l.Cf\a lO.n and 55.7S reapeet1vely ee w" expect.ed. . HO'IIe>r.r. ill !tUn no. 8 t.hen! wao na dacre .... in the sorUt\i co.r.tic.1ent. ill the a!r!ho~ zon.. III &ll Wre. runs t he 80rtina co.Uic1ent decreued o ... er the cmplet.e buch 1e/11th;.e.g.64 .~%, 67 .6 • .• nd '2 .~ in Runs no. 6 7 WId 8 respftCti'vely.

1il 1IWmIlJ,)" th. ruult.ll obL.a1ned in the .&d11ocnt eorti1ll: e"P.ri-1I!t!rIt.e ant:

•• A progneai .... chana' in eed..bent eiu i.e indic.ted u the b r ulcer u appro.ched . Bectnning.t the llaIt ar w .... e-induced .~efit. lIIOt.ion t.he IlleAn diam.ter increun 1101111. pr_ably by th. ItOrting I18'Chant .. d,"elaped here.1n. unt.U • point. 11 reached .t. which (pr.ewaahly) !.he e!recte or t.h. breaker are telt. and att.er wtdch t.tt. mean d1_t.er ~ecJ'8"1tS du. to • r.oYal ot u.. coars ... tr.ction ..r the u!llple.

b . The ~egree or sarline of the 11DIIP1e beeaaee ProlH,,,bel1 better iD the <>N~rl! cI1rec:t.ion.

"

z -f ~

~ -Ir w .... w ::; <l Cl

Z <l W ::;

" ,

,

Fi£!;u'e 211 . ~on or I'I~ Di .... t.f:r UId SorUrc Cottttio:i@CIt.l wi tb BYclI P(>II1 Uon

-"' ci -....

.8 ~ '-' u.

•• u. w 0

1.2 u C> 1.0 z .... Ir 0 Vl

02

SAND PARTICLE SIZES IN NCI-ES

SAND PARTlCl.E IN INCHES

Filii'" 2$ . ec.rpllrhon of lnit.1al .rod I"1n&l SJ.z~ P'r<!quf'"n"y Iib\..r1bu:tion or TDtal S...,., SMpl ..

"

e. Dillt.1nct peak, (1IOda:l Bi l8!) aN abu~M&d Sn t.h~ f inal .1& .... frequent,. di.sLr1bu. t i ona .

J. su-a..,. of data for Runa 00 . 6, 7 and II 18 given 1.n Tab)e m.

TABLE m SUMMAlIY c»' TEST C<lNDI'IlOII8 FOR SEDIMENT SCi!.nHG &XPElUMEN'15

""''" ... No . 6 Run No . T Run Nc . B

TOTAL mre Hr, . 101 "" 139

T ,~ . 3.00 ,.04 3.00

, ~ 52 .12 51 . J<> 51 . 20

WA TER T94P. ·F 51.3 ".0 65.2

H, in . ) .0) , .... 2.91

R, in . O.J<> 0 . 22 0 . ))

IS 0 .10 0.075 O.ll

L., ". 46 .08 47 . )2 46.08

',. in . 2. 78 ' .10 2.. 70

'""OJ SUlFE 1:20 1:20 1:20

60

VII SllM!W{Y AH!J CONClllSlONS

.. theoretJeaJ analyll1e i~ prUS'lted 10Ihlch dellcr1b~8 t.he eqtIll1~ hrlum ",raUb cf a nnd bead! 111 th" otrllhc>re 1Iona beyond t.he rll1lf:a cf eppreciabl" braaker in!luence and certain expected characteristics Qt tha ... av~- il'\dl.lcad ahe sorting or sll<llinent.ll in t.he su. arn .

The theory- 10IU devel oped in:. earlier cQNIideut..1onJ1 at t.he mechanics of wave-induced. motion of lingle sphef1.,,&l particles on pl..an", Ttnlghaned, iapenneable beache6.

S8parate pro!lle and sort.ing expe~tl were conducted us!nc two~diJlleDalonal beachu or natural s.nd 1n order to det.el'flline the oegree or ~pLlcah1l1ty of t he theoretical ralationships.

The tollClting concludona are drawnl

l. Ths 1..'l$Orat.lcal :1nl'lIst.ic.tiona yiald the rollowing r "Lu..1oJIP ship" tQr parUcle &118111 sLtt1." inst.ab1.llt.y ( the 1nc1pbtlt. abe, Dil , and f or the stu 111 o"clllat.ing l!qu11ibriWII (t.he equillbrium she, Dal;

• ( Sr ) r, «/t,,) (I-X) ($,) 0, -256.1 V lit o (i)1/2 g s, - Sr .",,, --~

.... 7 ,

De ~ [ 6 .81 HIQ~(1~)() ,

( St) f1 (d/b:,) ] '[;']~5J) s, 3" - 8In ""

2. For buehe" havinK ""lIent.1al1y a constllJlt sand IIba, !q'.luiona (52) and ( ~)) have been found to predie~ the depth at wb1ch ;:. r of ile mod1!lcation hepns wi tidn an a""lraga error Qt lass than 10'; tor th" ~ wava, t.a,ted.

) . FQr l)ONltlUl~ sand size and Y1tJ1 OC • OC: o ill £qt . (52)a.nd (!H) the -incip!ent. dQPU.- and 'eqtUlihf1.wa deptll.· may he c-.leu .. t'" !Qr ~ given 1oIaV8.

"

U the p.o1nt. of ln~lcrt. aMi_nt. .. Uon 11_ ott-ahor. nt Ute point. ot .qII1.l1bn_ s..n.ent. II)UOI:I, u.. b...:h tonu s steep bu.1ldini: orta~ profU. 0UId the .. DaN ut.r1lll1 ty of tbe pTOtu.. .,.,!Meatlotl 11 ~\'8n by th. IIQlI1libn_ dlptb.

It IJIe incipient. point. 11_ OIlIIhoNl ot tbe ItqIIli1br1_ point., U. bMeb rOTM s rlat, dici1-nC ot.rebo:-. pTOJU. and U:. ine.1phnt. deptb 1a U. 1I000aN atrem1 ty of tlIa p:-otlle IIOd1.tleaUon.

Clu,1I1eatLOlI ot profiles U411ng tbe above eontidllZ'at1one b "hown to acrM tOT t.br'oo out ot tho to\ll' t.aate with J0hn8on' . (1) a.p1rieal oep&.r&tion ot -.\lII:I!II,U'- and "win"tftr - prof'il ... eeord1nc tQ \he 1.neidomt. dlOlp-",.tft:r "'&1'0 steepnell.

4 . The theoratiru pr-otu .... (£q. 51) pn pod quillt£t.1 •• and uuonah1. quantlteUv. au_nt. vi th expG'iJrIent "'~r. breaker all.cte M,y' be ignored. In cen-ral t.l\e tIleoreUeal protllM ..... ate.per tha.'l UI. experlllumtt.1, the...n.u. alTO:' obIaTYC in dope be.1ni. 140 0,0 tor a glven dtoptll at. point. near tbe oft.$hor. bar.

Thb deviaUon 1.a cOT1lllatent. with .ct.lal uar-bot.u. na.1d .... loci U .. PI&l.lGr' than prlldietad by ... .uabl. Ulaorr.

S. 'DIll IIQll1llbriWII pro!1l. ot a land beach appean to be dtpendent ~on it... initial alop. (i • • • it... hi.tory) to an e.xtant not pradlctecl by the theory an4 in ..... nnllr not yet. ondorat4od.

6. \Ii& .... 1nducad afl<llillent aort1.na haa an ohI< ....... ad ( though w .. lI: ) tend.ncy to produc. a bl....odal aile-frequency dUtribution .In Ule otI.bora lOon. as 1s pr",ueted by tha th.ory. QuantU.Uv. au_lint. wiUt the theoreUeal modal shed, D.and 01' vu riot (OOd hcwlIVer.

7. 'nIotory pTftdiota qualitau.oq an iIlcr.ue in rlltI&II 1Ied1-BCl t di_ter with di.l1,.anc. in thIt onahW'll d1:lIcUon . D::parime'ntal. ver1r1""Uon o! Wa 1a tound onl,y .1. tha eO&lOaN utzedt.7 ot th. beaehea '-toed.

B. Theory and experiment both lndicate &II !nerene in the degr-e. or aortlni in the OlIIhore d1re;ctl.on . Her ..... &1n the theory dou not yiald a qWlllUtaU.e Nlaul.t.

"

' ... thoe", DPe",'-aU Ir' •• .,.. rOo deflao! tM etl,,-~, .f thoe bre.~"', bott_ r ... pa. ...... "'t"' .... '1Id nolllla, dcptlll _ tile "11'11,,1 dll­n tba ttoa .f held ••• tUMpo.-t .. Iodtl ....

Tbu lII .... ni,.H __ • c:.rrUd 0111 It the H,.d.rDd,.nlalu LaborltDr,. Df the Depart.nt of Chll .ndo Sanitu·,. In,u.ulll.& Df tba M .... e.!tueetu Institute . r Ttehoolo.,. Under Conlr.~t MOo. DA-~9-0" __ nr-16 .Ith lhe aeaeh Ir •• lon aoa r d., Corps . , In,lnc ... '" U. S. Ara,.. Contr.~t 'dalnl­Ilfltlan w .. pr ... lded 'OJ' the Dldl l on.f SponN,ed " ... Iurdl.f /II.l . T. Intu DSiII. 6"1.

on.. ilIAd' ..... WIdIr 1M d irection . f Dr. Anhu, T. tppen , "'or... .. lor of H),dfluHu Ind (III teo;bnlc:al 'up.nldon of Dr. Peter S . 11,11_ • .... I.hnl ' '''.f .... , of H.,drauHc I!qlneulll,. The expert_nul _I' oa Iq"Ulbrt.. pr-ofUel Ind al" _till, WII' pufor-.:!, l.r It. _It p'H, '" .......... Bud: G.lenDe and John ". Dracup , ""aplett •• l)" a ... arc:.h A .. lattaU .t tlte H),cSrodflU.1c1 LabOl"ltor ), •

. ,

I

1. Ippen, A. T. and. Eql.son, P. S., .... Stuc!y or 5ed1a..,.t. Sort.1.tli by w .... Shoalinl 0lI .. Plane 8e&ch,· Beach Erodo3rl Board Technical Xsorf.ndwll No . 63, WuMngt.on, D. e., 19$5 .

2. Eq;hllatt., P. S. , and De&JI, R. 0., "Wave-Induced Kotion of Discrete Botto. Sed1aant. Particl.,, " Proceeding, A.S. t .! •• Vol , 85. Mo. HI 10. Octohef', 1959 .

J . Tanner. W. r., "The Equll1bnum Such". GeophYlli cal Urdcm, Vol. 39. No.5. pp.

1.. Ou..Ucher, Ander, ·Coutal and Suburllle Kor,:ot.o1OC . · John 'oI1.l.,- '" Sons, 1958.

5, Jowen, J. \II •• "1116 Supply u.d Lou or Sand to thot Cout. . " Proceed:i:p at A,S.C.It •• Vol. liS, No. W ). S"Pl.. 1959.

6 . K.tU..r , R. L. and Zeiclar, J. M. , "I. Modal R..:lat.1ng ilylwl1ca -.nd Sed1mant htt4m in lquillhri_ in the Hellion ot Shoal1.n& Wavy , 8 ..... 11., .. ton., and Fore.tlore, M The Jovn>a.l of Geolop., Vol. 66. No.4, pp. b17-4hl, July. 1958 .

7. H&J'w, s~;.f.~r~ .... " No. 5. Iyoto,

II. SUvut..r, R. , "En&1nMI"infI A .... ect.a ot Coutal Sed:l..otBnt. ,",o •• ..,t.." Proeeedingll ot A,S,C,It" Vol, 9. No. R~ J, Sept. 1959.

1<). Scott, T., "Sand Mov_nt by ;,'avu," Such Eros10n Techn1c~ Mtnor&ndlmt No. 48, J.ugD.Bl 19%.

U. Rec~r. R.l. . , -Laboratory Study ct Equ1l1br1Jm Profiles of Be.ch .. ," Beacb Erosion ao.rd Technical K_rand!lII\ Ho. ill, Augu.t.. 1954 .

12 . Bue"", Slope, • Mo. 6,

Bet.w~en Sand Si~~ Qnd Beach- Face Vol. )2,

..

IiEl'!B£'l'ClS (CoDt.)

1), 8ai.nol.d, 1...1. " "San4 Mov_t bT W.v .. , be SIullo.,Scel, D:per1Jo.,U with SMd at Very Ww n..a1ty,. ofClUNl or: lot.. !.Nt.Hute at C1Ytl i":tg1.neer!. Vol. 27, tIP . 447, 19l&7.

:u.. t:,. W.t.al' W.v .. ,·

15.

16.

11 .

Vol. 29. No. S,

Eaglell<l<l, P.S ., Dean 11 .0., &lid Parelt. , l.A., "The 1'Iec:hen1cI of t.ke KotioD of Dberete Sphericel Bot.t.e. Sed.1..,t. Particle, Ou, \.0 ShoallJl( IoIlves,· Beach Ercdon Board T.ehnicel I'I-.onncn. No. 101.., Wa.shini;Wn, D.e., 19,1.

11, H. , ·St..t111t.,t of O$cIDuory ~ now alOl'll • Will , " Such Erosion Board ieehnic&1l'1lftOrand"", No. h1. Jill),. I9$!..

18. Kanch&r, M" "Mechanica at BottOll s.d.iII .. l l'Io'I_ent. du. t.o WllYe ActIon , ' Beacll Er-odon Board Ter.tm1cel M_oranliw! /10. 1S. JUIlfl, 19S5.

19. Jial.k.ani.l!, G. , "1'url>Ill...,t Flow nelll" an OleID.tllli 'Well." ~ Erosion 8o&n1 Tec:hnical !'I....,randwII No. 97 , Jul,. . 19S7.

20. In/D&n, D.L. , !'I..ehan1eo, " pp. 51-10 .

n. Sate , S., &11<1 lillhi, T. , Bed Kat.eria.:. ctu.e to ..... ". loIorlr.a l!8ofll..-.:h Innltuu.

In the ot Plilid Vel. 19. 1(0. 2.

~ ... " " 22 . Cart;t', J.J., ~r., "lIuhtane. eo.tfic1enu tor Spherel on. Plane

E\oIInt;Iary,. ':hu1a 8\lbodtt..d to the 1I.I .. ..,hu .. tt. wUtut., fit Techno1ocr fer til, deere. ot II.S., M.l.t., c..brida;', M .... • eh.iutt.8, PI6,y, 1957 . (l1npublhhed)

WeT" and D.uTent.a," 28, (l), pp. 261&, 1896-97,

'4 .

"

25.

Other- PeTtillent \lork Not. Spee1!1cllll R.t'rTd To

26. Olanne , "Bud, "Orf,hore Pl"otU_ ot Iqu1.Ubr1.1D11 BM.eh •• bl !hoo.,.,. alId IXpe!1JMn,,", S.M . Thui. , C<n!.r •• I, M .... aehu,.t.u lnatitute ot TK.bnolOO, 1959 (UnpubllIMcl.)

n. Draccp, John A .• "£qu.1.llbrlua OIUKter1.nicl ot Si;od kadI •• in WIe OU,1len z.one-. S.M. !bUJ.I , eo.w., It KM .. cbll. .. t.t.II In.Utllt~ or T""hnolOD _ 19EO (unpubUahe4)

..

• ___ ...... c.a.. <. I. _ . • - •• >. C ' . ... . ............ 11 • 1- _.,. __ . ~ ......... .... -... ,. ' .... "' .. , .... .., ... • . ""',_ ........ •• --.-.... .o..I"~Jao ......... , .. , ......... CI &Gr. L. '. " ... -_ ... "IDn. __ ~""""'" _._ • ) . ,-_ ....

'1111 _ .. l«1li , ~. I ...... _. t. ,,'"- _ .. _ ..... ---.- ...... ..... _ ..... - .......... ...... -,. '. .. ~ ... ..... ...... . ....... '. ".-.' ... .... I ... c..-- ." ................... ' . 1 .... _. r. • • .. u .... H. ~'-... .. " .... II . 10.-. t. ..... /CAL __ ,I}. ... "' ..... _. J • . Tlc."r ... __ "' ... II' ... _ . I." WS" .... tt· ,.. n.1o !$W'!'. ... ,." 10 -"-' ..... ' .... ....... ~, "'" . __ .. , -. .... , .. ..r no ,-' .... _ •• _ . ..... _ •. qo< ...... . , '--" ..... -• .... , .... -.. "', ................ , -.~ .~ .... "',-. __ . "'4000' -''''''- ,...., ... --_., -,~ ..... ..,,-. '-..........

'0 t." , ..... " ....... y oJ ........ "" "lA' ,,~ ..... ,. , ........ ,- , ..... no .""k ........ '" ....... -.-- ...... , .... -.... , ...... • _", .............. tI ..... oJ ........... -- .......... "" "Uf ..... • _ ...... _ .............. '" .. _ .... J _ ........ _ ",,"""', ... _, ... ,,_ .... ", .. _ .. II ........ _ ........ , ............... ..." ......... _11' .. _ .. ,_ ...... _.'* .... , _ ..... ,.,.-_ ... - .... ,,-.......... -... ... "" .. _ .... _ o .......... -'." ..... -. -"'" -"_'11"-_- , .......... .... , ... " _ ........ _II', _ ............. • .... If. -' ........ ,., .... .. ....... " _1110"" ... ,. '"'.' __ ....... _ ....... , ..... _ ......... _.-1._." .. , ......... '_.f ..... ,.. ....... .... , .. .... ..... _ .... - _II." ... ........ ,_ '" __ u , ... , .>f • .,,,. -1./ ... " .. • n' _ ...... ,'''" ....... <11 .......... ,,--, ... ,- .. _11_ .... __ .... ............. . ... _U .. " __ ...... of • ,,- .... ,_ ...... _ ..... " ........ " .. ~ ~ ",.! ... ~. " rM . ., ... ' ... --. _ •• 10." .. _ .... No oj ....... - .. -.. " ......... ,,_, ........ oJ .... , .. _,,, ........ .... 1.0 .... ". .... _. .... .... _. .. " ... oj ..... Uo _,,, ... -. ..., ..... _, . "'.to ....... _111."" ........... , ...... , ... - .. 10< ............ ",., ........ ~ .. , ... " .... _" ... ' _w .. _ .. _ ..... . . ~ ... , ...... ... _ ....

..... 01 .... ""-' . .-" '-'''' ~! ,._., ......... , .. _ •• 1<0( ..... _ '--_ ....... , ... .., "-' ,. ___ a<, .110" , ___ • .,-_. ..,,01",,_.

_ .. _10'0 ......... _ .... II. ' • ........... •• '. •• .... '11 .. _ ,..t •• n"co ... __ '" c ....... '. • ..... _ .•• r. '. &.,11 "" , .. ,. .....

'. _ ....... - •• ro .... '. $H,_, ...... -......... , .. """"""". d ..... '" "'.' ....,. .. ,_ '. '- .. _ .... _ , ....... <:11 .... _ ..... ." IM".--'" .. , '-- • .... , '"fW''' ,... ...... ..... _. I • ..- -............ ... ........ _ .. '. I .• "'._.'.0"_ _ .. _ ....... _ ,. '. .... " .. ." "" ........ . "~"" ' .... , ...... '. " .,., J. '. .. .,... J'" , .. ,_ ....... I ........ '. .. ... _. t. s. nIH ... T'. '10_. '. .. 11.0.. •• ... "-... ,..,...:.0, .0- .... .. " < • ...... . J. ~. 'EI"""', 00«II'_" . .. m. ....... J ...

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