rijkswaterstaat communications

sutrench-model

two-dimensional vertical mathematical model for sedimentation in dredged channels and trenches by currents and waves

byI. c. van rijn of delft hydrau lics labo ra to ry andg. i. tan of locks and w eirs d ep a r tm en t , r i jk sw aters taa t

the hague, 1985

a ll correspondence and applications should be adressed to;

rijksw aterstaa t

d ien st ge tijd ew ate ren

hoo ttskade 1

p o stb u s 20907

2500 EX the h ag u e - the n e th e rlan d s

the v iew s in this article a re the au thor's own,

recom m ended ca ta lo g u e entry:

reco m m en d ed c a ta lo g u e entry:

rljn, I, c . vansu tren ch m odel : tw o-d im ensional vertical m athem atica l m odel for se d im en ta tio n in d red g ed c h an n e ls and tre n c h e s by c u rre n ts and w a v e s / l . c. van rljn and g. I. ta n ; rijk sw aterstaa t. - the hague: rijk sw aterstaa t, 1985. - 63 p.: II!.; 24 cm . - (rijk sw aterstaa t com m unications; no. 41) blbliogr.: p . '59-60.

Contents

page

S y m b o ls .................................................................................................... 6S u b s c r i p t s ................................................................................................ 8

1 In tro d u ctio n ...................................................................................... 9

2 Basic equations and simplifications for local suspended sediment 10

2.1 C on tin u ity eq u a tio n fo r co n s tan t w i d t h ................................... ¡02.2 C on tin u ity eq u a tio n fo r vary ing w i d t h ......................................... 11

3 Flow velocity profiles......................................................................... 12

3.1 I n t r o d u c t i o n ............................................................................................ 123.2 V elocity profiles fo r com plicated flows (P R O F IL E m odel) . . 123.2.1 L o n g itu d in a l flow v e l o c i t y ................................................................ 133.2.2 C o m p u ta tio n p r o c e d u r e .................................................................... 163.2.3 C a l ib r a t io n ................................................................................................. 163.2.4 V ertical flow v e l o c i t y ......................................................................... 183.2.5 Bed-shear v e lo c ity ................................................................................... 183.3 V elocity profiles fo r g radually vary ing flows w ith w aves . . . 193.3.1 L ong itud inal flow v e l o c i t y ................................................................ 193.3.2 V ertical flow v e l o c i t y ......................................................................... 20

4 Fluid and sediment mixing coefficient.......................................... 22

4.1 I n t r o d u c t i o n ............................................................................................ 224.2 M ixing coefficients for com plicated flows (P R O F IL E m odel) . 224.2.1 V ertical d is trib u tio n o f fluid m ixing c o e f f i c i e n t ..................... 224.2.2 L ong itud inal d is trib u tio n o f fluid m ixing c o e f f ic ie n t ............ 224.2.3 C a l ib r a t io n ............................................ 244.3 M ixing coefficients fo r gradually varying flows w ith waves , , 254.3.1 C u rren t a lo n e ............................................................................................ 254.3.2 W aves a l o n e ............................................................................................ 26

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4.3.3 C u rren t and w a v e s ...................................................................................... 274.4 E qu ilib rium co n cen tra tio n p ro f ile s .......................................................... 28

5 Boundary cond itions................................................................................ 29

5.1 F low d o m a in .................................................................................................... 295.2 In le t b o u n d a r y ............................................................................................... 295.3 Outlet b o u n d a r y .................................................................................... 295.4 W ate r su rfa c e .................................................................................................... 305.5 Bed b o u n d a r y ............................................................................................... 305.5.1 Bed co n cen tra tio n f u n c t io n ........................................................................ 315.5.2 S edim ent flux f u n c t io n ................................................................................. 32

6 Bed level c h a n g e s .................................................................................... 34

6.1 E q u a t i o n s ......................................................................................................... 346.2 S uspended load t r a n s p o r t ........................................................................ 346.3 B ed-load t r a n s p o r t ...................................................................................... 356.3.1 G rad u ally varying flows w ith w a v e s ....................................................... 356.3.2 C om plicated f lo w s ........................................................................................... 36

7 Numerical solution methods and accuracy........................................ 37

7.1 Continuity equation for local suspended sed im en t......................... 377.2 Bed level c h a n g e s ........................................................................................... 38

8 Streamline refraction for channels and trenches oblique to thef lo w .............................................................................................................. 39

9 Sensitivity analysis of controlling parameters of SUTRENCH-m o d e l .......................................................................................................... 41

9.1 I n t r o d u c t i o n .................................................................................................... 419.2 Influence o f hydrau lic cond itions a t the i n l e t ................................... 419.3 Influence o f stream line r e f r a c t i o n .......................................................... 439.4 Influence o f particle fall velocity o f suspended sed im ent . . . 459.5 Influence o f o the r p a ra m e te r s ................................................................... 46

4

10 Verification of SUTRENCH-model.............................................. 47

10.1 I n t r o d u c t i o n ............................................................................................ 4710.2 M igration o f a channel in a f lu m e ................................................. 4710.3 S ed im en ta tion in a tr ia l d redge channel in th e W estern Scheldt,

T he N e t h e r l a n d s ................................................................................. 4810.4 S ed im en ta tion in a tunnel tren ch in a tidal river near

R o tte rd am , T he N e th e r la n d s .......................................................... 5110.5 S ed im en ta tion in a tr ia l d redge channel in A san Bay, K o rea , 52

11 Sediment trapping efficiency of dredged channels and trenches . 55

11.1 I n t r o d u c t i o n ............................................................................................ 5511.2 C o m p u t a t i o n s ....................................................................................... 5611.3 R e s u l t s ..................................................................................................... 56

12 R eferen ces..................................................... 59

5

Symbols

A coefficient ( —a reference level or bed -boundary level (Lâ am p litude of o rb ita l excursion (Lb w idth (LC C hézy coefficient (L0,5S _1c concen tra tion ( M L -3ca concen tra tion a t reference level ( M L -3c dep th-averaged concen tra tion ( M L -3D sed im entation ra te ( M L ^ ’T " 1D a dow nw ard sedim ent tran sp o rt at reference level ( M T ^ ‘L ~ 2D* particle size param ete r ( —d 50 m edian particle size (Ld channel dep th (LE dissipation rate of tu rbu lence energy (L 2T ~ 3E a upw ard sedim ent flux a t reference level ( M T - l L -2e sedim ent trap p in g efficiency o f dredged channels ( -g acceleration o f gravity (L T -2H wave heigh t (LH s significant wave height (Lh w ater d ep th (LK tu rbu lence energy (L 2T -2k, equivalent o r effective bed roughness height (LL length (LL s significant wave length (LN num ber of tim e steps ( -n num ber of vertical grid po in ts ( -P m ean sta tic fluid pressure ( M L -1 T -2p po rosity fac to r ( —Q discharge ( M L ~ 3S cross-section in teg rated sedim ent tra n sp o rt (volum e) (L 3T _1s dep th -in teg rated sed im ent tran sp o rt (volum e) (L2T ~ 1T bed-shear stress p aram ete r ( —T m m om entaneous value o f bed-shear stress param ete r { —T s significant wave period (Tt tim e (T

6

u local flow velocity in long itud inal (x) d irection ( L T " 1)Ü cross-section averaged flow velocity ( L T " 1)Û am p litu d e o f o rb ita l velocity ( L T " 1)

u * bed-shear velocity ( L T " 1)

Uh flow velocity a t w ater surface ( L T " 1)Um flow velocity a t m id dep th ( L T " 1)Vr cross-section averaged flow velocity in flow d irection ( L T " 1)W local flow velocity in vertical (z) d irec tion ( L T " 1)w s partic le fall velocity ( L T " 1)X long itud inal coo rd ina te (K)z vertical coo rd ina te (L)Zo zero-velocity level (L)Zb bed level above a ho rizon tal da tu m (L)

a coefficient ( - )«0 angle of ap p ro ach in g cu rren t w ith channel axis ( - )ß ra tio of sedim ent an d fluid m ixing coefficient ( - )Vb sm oo th ing coefficient ( - )7 angle o f channel side slope ( - )b thickness of m ixing layer near bed (for waves) (L)A relative density (under w ater) ( - )At tim e step (T)Ax space step in long itud inal d irection (L)Az space step in vertical d irec tion (L)Cf fluid m ixing coefficient (L 2T " : )

sedim ent m ixing coefficient (L 2T _1)

n coefficient ( - )K c o n tan t o f Von K arm an ( - )V kinem atic viscosity coefficient (L 2T " ! )

P density ( M L - 3 )a stan d ard dev iation of bed shear stress (M l _1T " 2)

dm c-averaged bed-shear stress ( M L - ’T -2 )i t tim e-averaged effective bed-shear stress ( M f - ' r 2)0 tu rbu lence-dam ping factor ( - )

I

Subscripts

a a t reference levelb bed, b o tto mb r b reak ing cond itions for wavesc cu rren tcw cu rren t an d wavescr criticalc equilib rium cond itionsf fluidh a t w ater surfacem a t m id dep thm ax m axim um valueR resulting, relatives suspended, sedim ent, significantt to ta lw wave0 a t in let b o u n d ary (x = 0)

1 Introduction

T h e construc tion o f a tunnel o r a p ipeline o r a new h a rb o u r generally requires the dredg ing of a channel o r trench in a river o r estuary . D epending on the geom etry o f the channel, various m orphological prob lem s m ay arise such as sed im en tation and erosion of the channel bed, local e rosion near the head of the tunnelelem ents p laced in the channel an d local instab ility of the side slopes of the channel,Especially o f im p o rtan ce fo r the client as well as the co n tra c to r a re the m orphological changes of th e channel bed, w hich are caused by a local change of the flow velocity an d hence the sedim ent tran sp o rt capacity resu lting in sed im en tation in the deceleration zone an d erosion in the accelera tion zone of the channel,As a resu lt of serious sed im en tation p roblem s w hich d id occur in som e large tunnel trenches dredged in the years 1960 to 1970 in the N etherlands, the D u tch Office for P ublic W orks (R ijksw aterstaat) has requested the D elft H ydrau lics L ab o ra to ry to develop a m athem atica l m odel fo r sed im en tation predictions, T he p u rp o se of such a m odel shou ld be the estim ation of the sed im entation in re la tion to the channel geom etry. This study, w hich sta rted in 1972 w ith in the fram ew ork of th e applied research p ro g ram m e o f the R ijksw aterstaa t, resulted in a tw o-d im ensional vertical m athem atical m odel for suspended sedim ent (S U T R E N C H -m odel), as rep o rted by the D elft H ydrau lics L ab o ra to ry (1975), (1977), (1980a), (1980b), by K erssens, P rin s an d V an Rijn, (1979) an d by V an Rijn (1980, 1984).In C hap te rs 2, 3, 4, 5, 6, a n d 7 of th e p resen t com m unications rep o rt a detailed descrip tion of the S U T R E N C H -m odel is given. In chap te r 8 the flow field in a channel ob lique to the flow is described. In C h ap te r 9 the influence o f the m ost im p o rta n t hydrau lic param ete rs on the pred ic ted sed im en tation rates is show n. Finally , an extensive verification analysis concerning flum e experim ents an d field studies is given (pipe line channel in the W estern Scheldt E stuary , the N e th e rlan d s; tunnel tren ch near R o tte rd am ; nav igation channel near K orea).F u tu ra l developm ents will be focussed on quasi-th ree d im ensional m odelling of the suspended sed im ent tra n sp o rt to deal w ith converging, diverging an d reversing flows,

9

2 Basic equations and simplifications for local suspended sediment

2.1 Continuity equation for constant width

T he basic eq u a tio n for the sedim ent con tinu ity of the tim e-averaged variables in the tw o-d im ensional (vertical) p lane reads, a s follow s (van Rijn, 1984):

de S 5 { d c \ d ô ( ôc

in w hich:c = m ean local concen tra tionu = m ean local flow velocity in x-direction (m/s)w = m ean local flow velocity in z-direction (m/s)ws = particle fall velocity (m/s)

£s,cw = ■ 1- fi.ï, u' — sedim ent m ixing coefficient for com binedcu rren t an d w ave conditions (im2/s )

= cu rren t - rela ted sed im ent m ixing coefficient (m2/s)= w ave - re la te d sedim ent m ixing coefficient (;m2/s )

X = long itud inal coo rd ina te (m)Z = vertical coo rd ina te (m)

Assum ing steady s ta te cond itions and neglecting the long itud inal diffusivetran sp o rt, w hich usually is an o rd er of m agn itude sm aller th a n the o th e r tra n sp o rt term s (van Rijn, 1984), E q u a tio n (2.1) reduces to :

d , , d „ , , d ( 8 e \ n_ ( « ) + - ( ( » - - £ ( v . = o (2.2)

E quation (2.2) can be solved num erically w hen the flow velocity, the sedim ent m ixing coefficient, the partic le fall velocity (assum ed to be a co n stan t param eter), the geom etrical an d physical boundary conditions a re know n.

F o r equilib rium cond itions | ^ = 0, ^ = 0, = 0 ] E q u a tio n (2.2) reduces to\ d x dz d x )

dec w s+ nSiCW— = 0 (2,3)

10

2.2 Continuity equation for varying width

A ssum ing the local flow velocity an d the local sedim ent concen tra tion to be co n stan t in la tera l (y) d irection , the suspended sedim ent tra n sp o r t in a la terally d iverging o r converging flow can be represen ted (to som e ex ten t) by in troduc ing th e w id th (b) o f the flow. A la tera lly varying flow m ay either be a laterally- b ounded channel w ith a vary ing w idth (river) o r a s tream tu b e w ith a vary ing w idth in a tw o-d im ensional horizon ta l flow field. In teg ra tio n of E q u a tio n (2.2) over the w idth , yields ;

| ( t a c ) + - ¿ ( i - 0 (2.4)

E quation (2.4) is the basic eq u a tio n o f the S U T R E N C H -m odel,T he w idth of the channel o r s tream tube m ust be know n a p rio ri (field o r m odel m easurem ents, o r m athem atical m odel results).

11

3 Flow velocity profiles

3.1 Introduction

T o solve E quation (2.4), th e flow velocity profiles along the tra ject m ust be know n. V arious m athem atical m odels can be applied to describe the flow velocity profiles, depending on the degree o f p e rtu rb a tio n o f the flow (large o r sm all bed level gradients).

F o r complicated flows includ ing those w ith flow reversal (steep sided channels), a refined m athem atical ap p ro ach is of essential im portance . A good rep resen ta tion of the velocity profiles can be ob ta ined by using a K.-Epsilon m odel, which is the m ost universal a n d widely used m odel for com plicated flows (Rodi, 1980; Alfrink and van Rijn, 1983; van Rijn 1983b),F o r lon-te rm m orpho log ical com putations, how ever, the K -E psilon m odel is no t a ttractive because of excessive co m p u ta tio n costs. Therefore, a m ore sim ple m odel based on flexible velocity profiles an d sim ple first o rd er differential eq u a tio n s was developed (P R O F IL E -m odel). A fundam ental d raw back of th is la tte r m odel is the need for em pirical d a ta over a wide range o f cond itions to ca lib ra te th e applied coefficients. W hen ca lib ra ted properly , how ever, th e P R O F IL E -m o d e i is a pow erful m ethod for the engineering practice (reasonable results for low costs).

F o r gradually varying flow s the app lica tion o f a soph istica ted m athem atical m odel is no t very efficient because the velocity profiles will be a lm ost equal to those in a h o rizo n ta l un iform flow. T hese cond itions can be represen ted sufficiently accurately by logarithm ic velocity profiles.

Since the flow cond itions in practice m ay differ widely depending on the bed level gradients, two versions o f the S U T R E N C H -m odel have been developed:

• model for com plicated flows w ithou t waves,• m odel fo r g radually varying flows w ith waves,

3.2 Velocity profiles for complicated flows (PROFILE model)

Since the ap p lica tio n o f a K -E psilan m odel for long term m orpho log ical co m p u ta tio n s is n o t very a ttrac tiv e because o f excessive com pu ta tion costs, a m ore sim ple flow

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m odel based on the app lica tion of flexible velocity profiles as suggested by Coles (1965), was developed. A m ajor d isadvan tage o f th is ap p ro ach is the need for em pirical d a ta over a w ide range of hyd rau lic cond itions to ca lib ra te the velocity profiles. H ow ever, w hen ca lib ra ted properly , the P R O F IL E -m o d e l is a very pow erful m ethod to com pu te the velocity profiles o f com plicated flows including th o se w ith flow reversal. T h e P R O F IL E -m o d e l is the basic m ethod of the S U T R E N C H -m odel to com pute the velocity profiles.

3.2.1 Longitudinal f lo w velocity

Coles (1965) show ed th a t the velocity profiles in a non -un ifo rm flow can be described by a linear com bination o f a logarithm ic profile rep resen ting the law of the wall an d a p ertu rb a tio n profile represen ting the influence o f p ressu re gradients, In the p resen t study a sim ilar ap p ro ach h as been used. T h e velocity profile is described by (see also F igure 1):

(3.1)

in which u = flow velocity a t height z above bed

= flow velocity a t w ater surface (z = h) = zero-velocity level (zo = 0.03 fcs)= effective bed roughness = w ater dep th = dim ensionless variab le = dim ensionless variable

(m/s)(m/s)

(m)(m)( m )

( - )( - )

uhZoKh

Á 2

T h e p ertu rba tion -p ro file F is represen ted by :

(3.2)

* X

Figure I D efin ition sketch.

13

T he A i - variable can be determ ined by apply ing the b o u n d ary condition , u = uh for z — h resu lting in :

T he flow velocity profile, as described by E quation (3.4), is com pletely defined when th e unknow n variables  u t an d uh a re specified. T herefore, th ree add itiona l equa tions m ust be specified, w hich are :

• equa tion of continu ity ,• eq u a tio n for the f-param eter,« eq u a tio n for the surface flow velocity (u,,).

CONTINUITY

T he w id th -in tegra ted d ischarge can be represen ted by :

(3.3)

C om bin ing E q u a tio n s (3.1) (3.2) an d (3.3) yields

u = A i u h In A Ui, 1 — A i In21

(3.4)

hQ = b J u d z (3.5)

in w hich :

Q = d ischarge b - w idth

(m3/s)(m)

S ubstitu tion o f E quation 3.4 in E q u atio n 3.5 an d in teg ration yields:

t-PARAMETER

A nalysis o f flow velocity profiles m easured in a channel perpend icu la r to the flow d irec tion (Delft H ydrau lics L ab o ra to ry , 1980a) show ed th a t the m id-depth velocity a t each location is approx im ate ly equal to the m id-dep th velocity of a uniform (equilibrium ) flow w ith the sam e flow velocity an d w ater d ep th a t th a t location.

Thus:

WmW - depth ~ ^mid- depth, equilibrium (3.7)

The m id-depth velocity is assum ed to be described by E q u a tio n (3.4) resu lting in :

, , f Q'5h ium = A í Ui,\n ( —— I ¡^2(0.5)' ■1 — 4 i In ( — ) II 2(0.5)' -(0 .5 )2J o j

(3.8)

The m id-dep th velocity fo r an equ ilib rium flow can be described by (see p a ra g ra p h 3.3.1):

1 7 k \ b h (1 9 )

C om bin ing equa tions (3.7), (3.8) an d (3.9), it follows th a t :

' h '1 + In 1 ^ .

1„(°-5hT~ = [2i2 +~37+T][2(0.5)r- (0.5)2'] ~ ° 'l6i2” 0,29< + 1,02 (3-10)zo

Figure 2 show s som e velocity profiles accord ing to E q u atio n s (3.6) an d (3.10) for a

given Q, b, h an d uh ind icating th a t the m ethod is capab le of represen ting a wide range of velocity profiles includ ing those w ith flow reversal.

SURFACE VELOCITY

T he sp a tia l varia tion of the w ater surface velocity is described by a sim ple first o rd er differential eq u a tio n w hich yields an exponentia l ad ju stm en t of the surface velocity to the equilib rium surface velocity (uhie\ as follow s:

dui, uh,e uh «a n 1 n7 - = a x - f - - 0i2 - r - « 3 -7- (3.11)dx h h b

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in w hich:

uk¡e = surface velocity for equilib rium flow (E quation (3.21)),h = w ater dep thb = flow w idtha i , « 2 , « 3 = em pirical (calib ration) coefficients

( m /s )

(m) (m)

( - )

IMI_C

JZ— o>— c* x:

>

!\

cj*

I ■ /

/i i *

t e

1r

' /i y

y i/ 1I

h =0.2 m/

),, . « i d

O =0.4 m /s z0 =0 .0 0 1 m

-1.0 - G 5 0 0 .5 1.0 1.5 2 ,0 2 .5 ► flo w v e lo c ity , y

uh = 0.38 m /s— ■ — uh = 0.48 m /s Ui, = 0,72 m /s uh = 0.96 m /s

t = 0.36t = 0t = S .42 1 = 1.42

 ! = - 0 .3 8 5A i = 0.162A , = —0.0145 A , = -0 .1 1 8

Figure 2 V elocity profiles according to P R O F lL E -m od el.

3,2.2 Computation procedure

E quation (3.11) can be solved num erically by using a sim ple R u nge-K u tta m ethod. T he surface velocity a t the inlet (uhy0) m ust be know n.T he com plete set o f E q u atio n s (3.6), (3.10) an d (3.11) is now defined an d can be solved to determ ine the A u t an d uh variables. U sing E q u a tio n (3.4) the velocity profiles can be com puted a t each location .T he inpu t d a ta for the P R O F IL E -m o d e l a re : discharge (Q), w idth (£>) an d dep th (h) along the traject, effective bed-roughness (ks), C o n s tan t o f Von K arm an (jc) and the surface velocity (u>,,o) a t the inlet.

3.2.3 Calibration

T he coefficients w hich have to be ca lib ra ted are the oq, a 2 a n d ot3 - coefficients of E quation (3.11). F o r th a t purpose m easured velocity profiles in a channel

16

perpend icu lar to the flow d irec tion were used (Delft H ydrau lics L ab o ra to ry , 1980a). Seven experim ents w ith various channel geom etries an d hydraulic cond itions (T l, T6, T7, T8, T13, T14 an d T16) were selected. Based on fitting of m easured an d com puted velocity profiles the « j an d a 2 — coefficients were found to be dependen t on the local b o tto m slope (dh jd x ), as follows :

« i = 0.28 + 0,11 tan h [6 ( d h /d x ) ~ 0.15]

a 2 = 0.235 + 0,065 tan h [17 (dh /dx -0 .0 3 5 ) ]

(3.12)

(3.13)

T he a 3-coefficient represen ts the ad ju stm en t o f the surface velocity to la tera l (w idth)

varia tions, Since experim ental d a ta were n o t available, the ot3-coefficient cou ld n o t be calib rated . Therefore, an expression is applied w hich yields a gradual ad ju stm en t o f the surface velocity, as follows :

a 3 = 0.1 tanh[10(tif)/dx)] (3.14)

E —^N

£O)'3

0.30

0.10

0 .2 m / s longitudinal ve locity M

'0 ,1 m / s v e r t ic a l v e lo c ity

- 0.10

-0.30

' ï I t-

t J J /■ifrSr i\i J / ‘

VV rjvw i^ ---------------- 1------------------------------ 1

0.00-> distance x(m )

d i s t a n c e x (nn )

com pu ted longitudinal flow velocity o f K -E psilon m odel com pu ted longitudinal flow velocity o f Profile m odel com pu ted vertical flow velocity o f Profile m odel

equivalent roughness = 0,02 m V on K arm ann constant = 0,35 discharge = 0 .1 2 m */s

4 m easured longitudinal velocity

2 m "

0.30N

+■>

Ol'5s z

0.10

* - 0.10

I -0.303.00 . 3.50 4 0 0 4.50

Figure 3 M easured and com pu ted velocity profiles in a channel perpencidular to the flow,

17

F igure 3 show s com puted an d m easured velocity profiles in a channel perpend icu lar to the flow (T14). T he agreem ent between m easured an d com puted velocity profiles is reasonab ly good in the acceleration zone bu t less good in the dec la ra tion zone of th e channel. T he results of a K -E psilon m odel are also show n. T he results of the P R O F IL E -m o d e l an d the sophisticated K -E psilon m odel show sim ilar dev iations com pared w ith the m easured values.F inally, it m ay be no ted th a t the experim ental resu lts show serious th ree- d im ensional effects, particu la rly in th e deceleration zone. T h is is ind icated by the specific discharge (per un it w id th) in the centre line o f the flume, w hich is relatively small in th e deceleration zone com pared w ith the value a t the inlet.

3.2.4 Vertical f low velocity

A pplying the (w id th-in tegrated) eq u a tio n of con tin u ity for the fluid :

i » a » d i s )b ox oz

the vertical flow velocity (w) can be com puted as (see F igure 1):

zi> + 2 Plu I db zi> + zw = - f Í u d z (3' 16>

zb + zn d x b a x zb+zo

S ubstitu tion o f E quation (3.4) and in teg ration yields a (com plicated) analy ticalexpression for the vertical flow velocity.

3.2,5 Bed-shear velocity

T he bed-shear velocity (w*) is determ ined from the flow velocity com puted a t a height z = 0,05 h above the bed assum ing a logarithm ic profile in the near-bed layer (z < 0.05 h) as follows :

0.05 h

(3.17)

in w hich :

ub - flow velocity a t z = 0,05 h above m ean bed (m /s)te = C o n s tan t o f Von K arm a n ( - )h = w ater dep th (m)z0 = zero-velocity level ( = 0.03 ks) (m)

18

3.3 Velocity profiles for gradually varying flows with waves

F o r g radually vary ing flow cond itions (say dh/dx ^ 0,05 an d db/dx ^ 0.05) the app lica tion of a sophisticated m ethod to com pute the velocity profiles is n o t very efficient because the velocity profiles wil a lm ost be equal to those for a uniform (equilibrium ) flow. I t is assum ed th a t for these cond itions the velocity profiles can be represen ted sufficiently accurately by sim ple logarithm ic profiles. T he influence of the waves on the (tim e-averaged) velocities is n it rep resen ted in the present study.

3,3.1 Longitudinal f lo w velocity

T he logarithm ic velocity profile is rep resen ted by :

S ubstitu tion of E q u a tio n (3.18) in the con tinu ity E q u a tio n (3.5) and in teg ration yields :

(3.18)

in w hich:

A x = roughness param ete ruhte = surface velocity for an equilib rium flowZ(f = zero-velocity level ( = 0.03 /cs)ks = cu rren t-re la ted bed-roughness

(m /s)(m )( m )

A pplying the b o u n d ary cond ition : u = uh a t z = h, it follows th a t :

(3.19)

(3,20)

S ubstitu tion of E q u a tio n (3.19) in E q u atio n (3.20) yields:

T he bed-shear velocity fo llow s from :

A i Ut,1 “ fi.e K(3.22)

resulting in :

“ A i KUk e ~ <L, . ( h \ bh

- , + l n U

(3.23)

E quation (3.23) yields sim ilar results as the follow ing (w ell-know n) expression :

,90,5 QC bh

in w hich :

g = acceleration of gravity

C = 18 log = Chèzy coefficient

(3.24)

(m /s2)

(m ° '5/s)

3.3.2 Vertical ß o w velocity

A pplying the w id th-in tegrated equation of con tinu ity :

1 d(bu) dw _ b ôx ^ dz

the vertical flow velocity can be com puted as :

du , 1 db Zt+Zw = - Ï J u d zZb + Z0 Zi + Zo

C om bin ing E q u atio n (3.18) an d (3.26) it follows th a t:

clA iw

H.+ u h,e d x

Aí utl,e In■ \dh

zq) dx

+A í uj,.,

z — h — z In I — ) + h I n f —2 o / \ zo

db Q dbd x b 2 dx

(3.25)

(3.26)

(3.27)

20

in w h ic h :

dith'Qdx

u dh f h \ d ü ft dx + n \ z 0/ dx

- 1 + In¿o

M i n i ­no. dh

d x

d A \dx

d adx

u =

1 + In [ —

dh

r í ^ w 2 dxh iB -

_ VoJ-

I dh 1 dbbh2 dx b 2h d x Q

Qbh

(3.28)

(3.29)

(3.30)

(3.31)

In case of a varying w idth b u t a un iform d ep th (dh/dx = 0) E quation (3.27) yields a zero vertical velocity.

21

4 Fluid and sediment mixing coefficient

4.1 Introduction

T he sedim ent m ixing coefficient is rela ted to the fluid m ixing coefficient as follows :

Es = ß< l> Sf (4.1)

in which :

cs = sedim ent m ixing coefficient (m 2/s)F,f - fluid m ixing coefficient (m 2/s)ß = ra tio sedim ent m ass m ixing an d fluid m om entum m ixing coefficients ( —)(j) = tu rbu lence d am ping factor ( —)

T he jS-factor represen ts the difference in the diffusion (or m ixing) of a fluid ‘particle’ (or sm all coheren t fluid structu re ) an d a discrete sed im ent particle an d is assum ed to be co n stan t over the w ater depth . Based on experim ental d a ta of C olem an (1970), the ß-factor was found to be in the range 1 to 3 (van R pn, 1982a). T he (^-factor expresses the dam ping of the tu rbu lence by the sedim ent particles resulting in a reduction of the fluid m ixing coefficient. This effect was studied by van Rijn (1982 a). F o r concen tra tions sm aller th a n 10,000 mg/1 the influence of the (^-factor is relatively sm all an d m ay, therefore, be neglected for m ost p rac tica l cases.

4.2 Mixing coefficients for complicated flows (PROFILE-model)

Since the co m p u ta tio n of the fluid m ixing coefficient by a sophisticated m athem atical m odel (K -E psilon tu rbu lence m odel) is no t a ttrac tiv e for long-term m orpho log ical co m p u ta tio n s because of excessive co m p u ta tio n tim e, a m ore sim ple m ethod based on the app lica tion of flexible profiles was developed, F lu id m ixing coefficients com puted by a K -E psilon tu rbu lence m odel for a lim ited set o f hydraulic cond itions w ere used for ca lib ra tio n of the sim ple profile-m ethod.

4.2.1 Vertical distribution o f fluid mixing coefficient

In vertical d irection a parab o lic -co n stan t profile is used w hich m eans a co n s tan t

22

(m axim um ) value in the upper half o f the d ep th and a p a rab o lic d is trib u tio n in the low er ha lf of the dep th , as follows (see F igure 4):

s / , m a x I 1 -------—2 z \ 2

for Z- < 0.5 (4.2a)— £ ƒ , maxh

Cf ~ Ef ,n w x for y ^ 0.5h

(4,2b)

~ ß (4.2c)

£ f ,m a x

Figure 4 Vertica! d istribution o f fluid m ixing coeffiçient.

T he reason for app ly ing a co n s tan t it/-value in the up p er half o f th e d ep th is th a t it yields a finite co n cen tra tio n a t the w ater surface and m ore realistic concen tra tions in the u p p er p a r t o f th e d ep th (van Rijn, 1982 a). T he p arab o lic -co n stan t d is trib u tio n was in tro d u ced by K erssens (1977).

4,2.2 Longitudinal distribution o f f lu id m ixing coefficient

T he varia tion o f th e m ixing coefficients in long itud inal d irec tion is effectuated by varying the e ^ ^ - v a l u e apply ing a sim ple first o rd er differential equa tion , as follow s :

I II III

■f,m ax (4.3)

in w hich:

Ef,max,e = 0.25 K u%¡eh = m axim um fluid m ixing coefficientfor equ ilib rium (uniform ) cond itions

uh — surface velocity accord ing to E q u a tio n (3,11)Ü = cross-section averaged velocity

(m 2 /s)(m/s)(m /s)

23

= bed-shear velocity for equ ilib rium cond itions accord ing to E q u atio n (3.23) (m /s)

K = C o n s tan t o f Von K arm an ( - )h ~ w ater dep th ( - )«4 , « 5 = em perical coefficients ( —}Term Í represen ts the decrease o f the value tow ards its equ ilib rium value. T erm II represen ts the increase of the e j im8X-value after a change of the flow velocity profile. T erm III is a stabilizing term ac ting a t steep sloping bo ttom s. E quation (4.3) can be solved num erically for a given e ^ m0JC-value a t the inlet (X = 0).

4.2.3 Calibration

T he a 4- an d a 5-coefficients were determ ined by ca lib ra tio n using m ixing coefficient d istribu tions com puted by the K -E psilon m odel for various channel geom etries, yielding :

a 4 = 0.05 «s = 0.015

F igure 5 show s som e ca lib ra tio n results for a channel perpend icu lar to th e flow. G enerally , the values of the K -E psilon m odel are som ew hat sm aller in the upper half o f the d ep th and som ew hat larger in the low er half of the dep th , particu la rly in the acceleration zone. These deviations d o n o t seriously influence the pred ic ted sed im entation ra te s of d redged channels (van Rijn, 1984).

10.20

0.10

'VIA 0.2 0.8 w*w-------

0,8 0.42.4 m

com pu ted by K -E psilon m odel com pu ted by P rofile-m odel

Figure 5 C om pu ted fluid m ixing coefficients for a channel perpendicular to th e flow

24

4.3 Mixing coefficients for gradually varying flows with waves

In case of a g radually vary ing flow {dh/dx < 0.05, db/dx < 0.05) it is assum ed to be acceptab le to use sim ple m ixing coefficient d istribu tions, as used for equilibrium (uniform ) conditions.

4,3,1 Current alone

F o r equilib rium cond itions the sedim ent m ixing coefficient usually is represented by a parabo lic d is trib u tio n ;

Es,c = ßKU*.cZ\ 1 - ^ (4.4)

in w hich:

w#|i = bed-shear velocity for a cu rren t alone accord ing to E q u a tio n (3.23) (m /s)

E quation (4.4) yields a zero -concen tra tion a t the w ater surface, w hich is n o t very realistic. Therefore, in th e presen t s tudy a parab o lic -co n stan t m ixing coefficient d istribu tion , in tro d u ced by K erssens (1977), is applied :

f‘s,c &s,c,m<tx ßs.c.max | 1 '2 z

for - < 0.5 h

= 0.25 ß ic m*iC h for - ^ 0.5

(4.5a)

(4.5b)

E q u a tio n (4.5) is show n in F igure 6 .T he ßs,c,max“Value is equal to the m axim um value o f the parab o lic d istribu tion accord ing to E q u atio n (4.4).

w a te r surface

5.C, m a x

T|4 (linear)

)= 2 ( p a r a b o l i c )

b<2dFigure 6 Current-related m ixing coefficients.

25

4.3,2 W aves alone

Based on the analysis o f co n cen tra tio n profiles generated by waves, the wave- related sedim ent m ixing coefficient was found to be (van Rijn, 1985):

es,w = cs,w,beJ , for z st <5 (4.6a)fiSj w ,max > for z ^ 0.5 h (4.ob)

z — Ô

in w hich:

3“ {£stw,max £s,bed) I q ^ ̂ ]> fot <3 < Z 0,5 lí (4.6c)

£s.w.fcc,¡ = w ave-related sedim ent m ixing coefficient closeto th e bed (tn2/s)

es,iv,t»<ii = w ave-related sedim ent m ixing coefficient inup p er half o f dep th (m 2 /s)

ô = thickness of near-bed m ixing layer (m)

E quation (4.6) is show n in F igure 7.

w ate r surface

Figure 7 W ave-related sedim ent m ixing coefficient.

M easured concen tra tion profiles were analyzed to rela te the characteristicparam eters of the sedim ent m ixing d istribu tion to general w ave param ete rs yielding(van Rijn, 1985):

£s,w,i>e(i = 0.00065 D 2 «i,r d ái,,w (4.7)

4*,*,™,* = ° '°3 5 abr ~ (4.8)* 5

5 = 0.06 (4.9)

26

in w hich :

(A a \ 1/3D * - iU<j ( 1 = p an ic le size p aram ete r { - )

K H s Ts sinh (2n h / L s)

ûb.w = i it \ ~ Pea*c villue o f o rb ita l velocity a t bed (m/s)

abf = b reaking coefficient represen ting the influence o f b reak ingwaves o n the sedim ent m ixing process ( - )

H s = significant w ave height (m)L s = significant wave length (m)7 / = significant wave period (relative to m oving co o rd in a te system ) (s)à = (p s ~ p ) /p - relative density { - )g = acceleration of gravity (m /s2)V = k inem atic viscosity coefficient (m 2/s)

T he b reak ing coefficient (ctbr) w as found to be dependen t on the relative wave height (van Rijn, 1985), as follow s:

a bt = 5 for ^ ^ 0.6 (breaking waves) (4.10a)

ƒƒa b, = 1 , for < 0.6 (non -break ing waves) (4.10b)

4.3.3 Current and waves

W hen a w ave field is superim posed on a cu rren t, the overall sedim ent m ixing is represented by a linear addition , o f the w ave-related an d cu rren t-re la ted m ixing coefficients (van R pn, 1985), as follow s:

es , c + cs,w (411)

in w hich :

Cs.cw = sedim ent m ixing coefficient for cu rren t an d waves (m 2/s)eSit = cu rren t-re la ted sedim ent m ixing coefficient (m 2 /s)Cs,w - w ave-related sedim ent m ixing coefficient (m 2/s)

WAVE - RELATED MIXING

I t is assum ed th a t the w ave-related m ixing is n o t m odified by the presence of a curren t. Therefore, E quation (4.6) is applied (see also F igure 7).

27

CURRENT - RELATED MIXING

Because of th e presence of waves, the m ean cu rren t velocity profile is m odified (van Rijn,, 1985). Therefore, it is logical to assum e th a t the cu rren t-re la ted m ixing is also m odified. T his effect has been represen ted by ad justing the m ixing coefficient (in the low er h a lf of the dep th ) of a cu rren t alone, as described by E quation (4.5), as follows :

2 z \ ' ' z4s,c ~ £$te,trtax ^'s,ctm ax ¡ 1 ) f o t 0.5 (4.12a)

«s,c = i'-s,c,„wx = 0.25 ßK U #iCh for ~ ^ 0.5 (4.12b)

in w hich:

¡I = coefficient ( - )= bed-shear velocity for equilib rium cond itions

accord ing to E quation (3.23) (m /s)

T he £s,ClW„ ~ value is n o t supposed to be m odified. T h e i?-coefficient is assum ed to be in the range t] — 1 (linear) to if =■ 2 (parabo lic) depend ing on the relative streng th of the w ave m o tion (th.,*,) an d the m ean cu rren t (w), E q u a tio n (4.12) is show n in F igure 6 .B ased on the analysis of m easured concen tra tion profiles, it was found (van Rijn, 1985):

n * _ o . 2 5 % ? + 2 , f o r 0 ^ % f < 4 (4.13a)1«! J«l

t/ » 1 , for ^ > 4 (4.13b)|u|

4.4 Equilibrium concentration profiles

A pplying E quation (2,3) an d the p roposed expressions for the m ixing coefficient, a concen tra tion profile for equ ilib rium cond itions can be com pu ted analytically or num erically (van Rijn, 1984),

28

5 Boundary conditions

5.1 Flow domain

T h e follow ing specifications are requ ired :

• in itia l (t = 0) bo ttom -level profiles along the tra jec t: zb = f ( x , t = 0)• W ater dep th along the tra ject : h = f ( x , t = 0)• flow w idth along th e tra ject : b - f ( x )

The w ater surface is assum ed to be horizontal. W ate r level varia tions du e to accelera tion an d deceleration effects are neglected,

5.2 Inlet boundary

T he in let b o u n d ary shou ld be selected a t a location w here n o o r m inor m orpho log ical changes are to be expected. F o r un id irectiona l flow th is location should be chosen as close as possible to th e area of interest. In case of tidal flow the inlet b oundary should be far aw ay from the area o f interest.T he follow ing specifications are requ ired :

• d ischarge :Q - ƒ (r)• flow velocity d is trib u tio n :u — f { z , t )• m ixing coefficient d is trib u tio n :c4 — f ( z , t )• sedim ent concen tra tion d is trib u tio n x = f { z , t )

Preferably, m easured concen tra tion profiles should be used a t the inlet (x = 0). Special cases are an equ ilib rium concen tra tion profile o r a ze ro -concen tra tion (no initial load) profile specified a t the inlet.

5.3 Outlet boundary

T he location of the ou tle t bou n d ary shou ld always be far aw ay from the area of interest. As the w ater surface is assum ed to be ho rizon tal, n o add itiona l specifications a re required .

29

5.4 Water surface

T h e ne t vertical sedim ent tra n sp o r t is assum ed to be zero, resu lting in :

(5.1)

5.5 Bed boundary

• flow velocity : w = 0 a t z = z0• co n cen tra tio n : ca specified a t z = zb+a, o r

.(5.2)

(5.3)

(5.4)specified a t z — zb + a

The bed concen tra tion (ca) as well as the upw ard sedim ent flux (E„) a re specified by functions w hich relate those variables to local near-bed flow, w ave an d sedim ent p aram eters. T he applied functions are presen ted in p a rag rap h s 5.5.1 an d 5.5.2. W hen the flow is varying rap idly , the app lica tion of a bed -concen tra tion type of bou n d ary cond ition m ay result in a positive co n cen tra tio n grad ien t near the bed (see F igure 8) w hich is physically n o t realistic. In th a t case the co n cen tra tio n a t th a t location (x¡) is recom puted apply ing a zero -concen tra tion grad ien t as bed- bou n d ary cond ition ( ô c jô z = 0).

Figure 8 P ositive bed-concentration gradient.

T he bed -b o u n d ary co n d itio n is specified a t an a rb itra ry level (a) above th e m ean bed level. It is a ttractive to apply a bed -boundary level close to the bed, because in th a t case the bed co n cen tra tio n (or the flux) can be represen ted by the ir equ ilib rium values assum ing th a t there is an alm ost in stan tan eo u s ad ju stm en t to equilib rium cond itions close to the bed. D etailed experim ental research has show n

30

th a t these assum ptions a re reaso n ab le .(Delft H ydray lic L ab o ra to ry , M 1531-1, 1981a; M 1531-IÏ, 1981b; M 1531-III, 1983a and M 1531-IV , 1983b).

5.5,1 Bed concentration function

GRADUALLY VARYING FLOWS WITH WAVES

F o r these con d itio n s a sim ple determ inistic function, as p roposed by van Rijn(1982a, 1985) for sand particles, is used. T his function rela tes th e equilibrium bedco n cen tra tio n (cflifi) to local flow, wave and sedim ent param eters, as follow s:

= 0.015 (5.5)a

in w hich :

( p s - P g \ 1/3-D* = d so Í ~ — ^ 2 ) = partic le size p a ram ete r ( — )

T = IhfOL— hïL = shear-stress p a ra m ete r ( - )Tb,cr

Tfe.cw = effective bed-shear stress for flows w ith w aves(van Rijn, 1985) (N /m 2)

Tfc.cr = critical bed-shear stress fo r in itia tion of m o tionacco rd ing to Shields (N /m 2)

d 50 — m edian partic le size (m)a — reference leve! (m)p s — sedim ent density (kg /m 3)p - fluid density (kg /m 3)g = acce lera tion o f grav ity (m /s2)y = k inem atic viscosity coefficient (m 2/s)

E q u a tio n (5.5) specifies a d im ensionless concen tra tion . M ultip ly ing by IO3 yields a co n cen tra tio n in mg/1.

COMPLICATED FLOWS WITHOUT WAVES

F o r com plicated flows w here flow separa tion an d flow reversal m ay occur, a determ in istic ap p ro a ch as expressed by E q u a tio n (5.5) does n o t yield realistic

31

results. In such flows the (effective) bed-shear stress in o r near the separa tion an d rea ttach m en t p o in t m ay ap p ro a ch zero resu lting in a zero-bed co n cen tra tio n or flux (applying a determ in istic equa tion ), w hich is n o t realistic in a physical sense. Therefore, a s tochastic ap p ro a ch is in troduced to rep resen t the influence of the velocity fluctuations close to the bed w hich have a d o m in a tin g effect o n the p ick­up of sed im ent particles near the sep ara tio n an d rea ttach m en t points.A pplying a stochastic ap p ro a ch (van Rijn, 1984), the tim e-averaged bed concentration ( c j can be expressed a s :

T he J i an d J 2 in teg rals as well as expressions for the critica l bed-shear stress are given by van Rijn (1984),

5.5.2 Sediment f lu x function

It is assum ed th a t the upw ard sedim ent flux a t the bed in non-un ifo rm (dü/ôx 0) cond itions will be app rox im ate ly equal to its equ ilib rium value for uniform conditions,

(5.6)

in w hich :

1.5

\J ll +1.5

\J2\ = s tochastic shear-stress

param ete r

ti' = s ta n d a rd dev ia tion o f effective bed-shear stress Tb'O- = m om entaneous critical bed-shear stress

(N /m 2)(N /m 2)

A pplying E q u atio n (2.3), it follows for equ ilib rium cond itions th a t:

E„ = - » >s ca (5.7)

GRADUALLY VARYING FLOWS

S ubstitu tion of E q u atio n (5.5) in E quation (5.7) yields:

(5.8)

I 32

COMPLICATED FLOWS

E a =5c

Csdz= —0,03 w,

dso T„ a D

1.3

0.3 (5.9)

F o r hydrau lic cond itions below those for in itia tion of m o tion , E q u atio n s (5.8) and(5.9) yield a ze ro -upw ard sedim ent flux w hich is specified as a zero -concen tra tion grad ien t ( d e jd z — 0).

33

6 Bed level changes

6.1 Equations

After co m p u ta tio n of the co n cen tra tio n field the bed level changes a re com puted using the cross-section-in tegrated con tinu ity equa tion , which reads as follows :

dbzb 1

I t + p . , ( l - p )dbhc ÔS'

ôt dx0 ( 6 . 1)

in w hich :

zb = bed level w ith respect to reference d a tu m (m)t = tim e (s)p = p o rosity fac to r ( —)b = w idth (m)h = w ater dep th (m)

1 z u + h

c = - J c dz = dep th-averaged co n cen tra tio n (kg /m 3)

S = Ss + Sh —■ cross-section in teg rated to ta l load (m 3/s)S s — cross-section in teg rated suspended load (m 3/s)S h = cross-section in tegrated bed load (m 3/s)p s = sedim ent density (kg /m 3)

A ssum ing quasi-steady flow conditions, the sto rage term (dbhc/dt) can be neglected.

6.2 Suspended load transport

T he suspended load tran sp o rt is com puted as:

Zf, + h

Ss = b ƒ u c d z (6.2)zi + a

34

in w hich:

z = vertical co o rd in a te

c — local co n cen tra tio n u = local flow velocity a = reference level

(kg /m 3)(m /s)

(m)(m)

6.3 Bed-load transport

T h e tra n sp o rt o f sed im ent particles below the bed -b o u n d ary level (zb + z 0 < z < zb-ya )

is rep resen ted as bed-load tra n sp o rt using a sim ple form ula. This schem atization im plies the selection o f a b ed -b o u n d a ry level (a) close to th e bed. In th e p resen t s tudy th is level is assum ed to be located a t the to p of the bed forms, T hus a j A b (Ab = bed-form height) w ith a m in im um value of a = 0,01 h for reasons of accuracy (van Rijn, 1982a),T his ap p ro a ch requires in fo rm ation of th e bed-form height, w hich can be ob ta ined b y m easurem ents (echo soundings) o r p red ic tions (van Rijn, 1982b). F inally , it is n o ted th a t the co m p u ted bed-load tra n sp o r t m ay be ra th e r inaccura te . T his, how ever, does n o t seriously effect the overall results of the S U T R E N C H -m odel, w hen the m odel is app lied for cond itions w ith a d o m in a tin g suspended load.

6.3.1 Gradually varying flow s with waves

F o r a cu rren t alone the bed-load tra n sp o rt can be represen ted by a sim ple form ula, as follows (van Rijn, 1982a):

G rav ity effects a t sloping b o tto m s resu lting in an increased b ed -load tra n sp o r t ra te a t a dow nw ard sloping b o tto m an d a reduced value a t an upw ard sloping b o tto m are taken in to acco u n t via the 7"-param eter.

In case of hydrau lic cond itions w ith cu rren ts and w aves a generally accepted form ula for the bed-load tra n sp o rt is n o t available. T herefore, the follow ing a p p ro a c h is used :

= 0.053 b (A g f - 5 d ia (6.3)

in w hich:

Sj, = b ed -load tra n sp o r t A = (ps - p ) / p = relative density

(m 3/s)

(-)

Sb = a b c a u„ (6.4)

35

in w hich:

a = th ickness o f bed-load layer b = flow w idthca = (volum e) co n cen tra tio n a t reference level (z = a) ua = flow velocity a t reference level (z = a)

(m)( m )

(-)(m /s)

T he th ickness of the bed-load layer is assum ed to be equal to the d istance between the reference level an d the m ean bed level. T he co n cen tra tio n s in this layer a re assum ed to be co n s tan t an d equal to the concen tra tion ( c j com puted a t the reference level. Is is realized th a t th is schem atization is ra th e r crude, b u t since the bed-load tra n sp o rt is sm all com pared w ith the suspended load tra n sp o rt possible e rro rs d o n o t have a significant effect on the accuracy o f the to ta l load tran sp o rt.

6.3.2 Complicated flow s

T he bed-load tra n sp o r t is represen ted by a stochastic version o f E quation (6.3), as follow s (van Rijn, 1984):

S* = 0.1 b {Ag) (6.5)

36

7 Numerical solution methods and accuracy

7.1 Continuity equation for local suspended sediment

T o solve E q u atio n (2.4), a finite elem ent m ethod based on w eighted residuals accord ing to the (m odified) G a le rk in -m ethod is used.The co n tin u o u s so lu tion (tw o-d im ensional) d o m ain is d iv ided in to a system of q u ad ra n g u la r elem ents. T he vertical d im ensions of the elem ents decrease tow ards th e bed to p rov ide a g rea ter reso lu tion in the zone w here la rge velocity an d co n cen tra tio n g rad ien ts exist, Between the nodes o f the elem ents th e u n k n o w n variable is represen ted by a linear function. T hen , for each elem ent the coefficients co rrespond ing to the u n know n variab le a t each node are determ ined . F inally , th e (tri-d iagonal) coefficients m atrix for the com plete so lu tion d om ain is determ ined , from w hich the coefficients can be solved (V reugdenhil, 1982). A detailed accuracy analysis show s th a t in vertical d irection a t least 10 grid po in ts shou ld be used for

n I-E

8_QO

Ci)'5

fws 1p* u* 0.5 c-= 0 .0 a ,, -

5^__=

i = (>05 0l1 —

0.2

u.o

O 0 2 0.4 0.6 0.8 1.0 1.

-j— >X (=Q 4 T# £ )I I t u n.

2 1.4

10 15 20 25 ► d istance, x (m)

30 35

analytical solution Hjelm felt and Lenati num erical so lu tio n (n = 15, A x = 0,2 h)

h ~ 1,0 m û = 1,0 m /s wa = 0,02 m /s u* = 0,1 in/s

K = 0.4 ¡I = 1ca = 1000 mg/1

Figure 9 C om parison o f analytica lly and num erically com pu ted concentrations.

37

cond itions w ith a cu rren t a lone an d a t least 20 po in ts fo r cu rren ts superim posed by waves. In long itud inal d irec tion a t least 10 elem ent lengths shou ld be used over the characteristic leng th scale of th e b o tto m profile (side slope leng th of a d redged channel).F o r a ho rizon tally un iform flow (w ithout w aves) the results o f the num erical so lu tion m ethod can be co m p ared w ith an ana ly tica l so lu tion . H jelm felt an d Lenau (1970) presented an analy tical so lu tion o f E q u atio n (2.2) assum ing a:• parabo lic sedim ent m ixing coefficient (E quation (4.4)),• co n s tan t flow velocity in vertical d irec tion anda co n s tan t bed co n cen tra tio n in long itud ina l direction .F igure 9 show s the resu lts of the ana ly tica l so lu tion an d the (present) num erical so lu tion for a specific case (wjßtcu.^ = 0.5). T he num erical so lu tion is based on 15 grid po in ts in vertical d irection , A x = 0,2 h an d a bed co n cen tra tio n specified at a = 0.05 h. T he num erical inaccuracy increases to w ard s the w ater surface w hich is caused by the variab le elem ent size in vertical d irec tion yielding relatively large vertical elem ent sizes n ea r the w ater surface. T he m axim um erro r is a b o u t 5 to 10% , w hich is qu ite accep tab le for engineering purposes.

7.2 Bed level changes

Bed level changes a re com p u ted from the cross-section in tegrated sedim ent tra n sp o rt (E q u a tio n (6.1)).F o r the co m p u ta tio n of the new bed level a t tim e t + At from the know n bed level a t tim e t the follow ing num erical schem e (L A X - schem e) is u sed :

4 ! / ' = 4 .* - ^ - 24. *+4. *-*«). t7-1)2(1 - p)psb Ax

T he y „-factor in E quation (7.1) determ ines to w hat ex ten t the bed levels o f the su rro u n d in g po in ts of z btX a re tak en in to acco u n t for th e co m p u ta tio n of th e new bed level zb¡ x a t tim e t + At. T h is causes num erical sm oo th ing a t sharps tran sitio n s of the bed level profile. N um erical inaccuracy is m inim al for a p ro p er selection of the (num erical) ys, N and At param eter.

38

8 Streamline refraction for channels and trenches oblique to the flow

G enerally , sed im entation p red ic tions are to be m ade for channels an d trenches w hich are ob lique (at an angle) to the ap p ro ach in g cu rren t (see F igu re 10),

approaching current

s in c to -v R,o

y

Figure 10 Stream line refraction in an oblique channel.

T he stream lines a re refracted a t the upstream a n d dow nstream side slopes of the channel. T he refraction effect is largest near the bed an d sm allest nea r the w ater surface. Because o f th e refraction effect, there is an increase of the cu rren t velocity w ithin the channel (converging stream lines). F o r a channel a t a sm all angle («o < 20°) the cu rren t velocity in the channel m ay becom e larger th a n th a t outside the channel.

>o T hi Side Banks

39

T he dep th-averaged cu rren t velocity in an ob lique channel of infinite length in in ­d irec tion ) can be described by the follow ing eq u a tio n s :

d (hí¡) oc o n t in u it y t— = 0 (8 .1 )Ox

áu 1 dp it,* AMOTION U T r-------- ß Sx -1------ = 0 (8 ,2 )

ox p o x p n

u ^ - ~ g S i + X. ^ = 0 (8 ,3)ox p h

in w hich:

it — dep th -averaged velocity in x -direction (m /s)V = dep th -averaged velocity in y -d ircction (m /s)p = dep th -averaged fluid pressure (N /m 2)

= b o tto m shear stress ( = p g v \ / C 2) (N /m 2)s = b o tto m grad ien t ( ~ )h = w ater dep th (m)p — fluid density (kg /m 3)g - accelera tion of g ravity (m /s2)

Boer (1984) has show n th a t bo th the convection an d friction te rm s are of essential im portance for a good rep resen ta tion of the flow field.A num erical so lu tion of E quations (8,1), (8.2) an d (8,3) is also given by Boer (1984). A pplying this ap p ro ach the ü an d ñ-variables as well as the local cu rren t d irec tion can be com puted.T he cu rren t velocities a long the refracted stream line can be represen ted in the S U T R E N C H -m odel by varying the w id th (b) o f the flow.

40

9 Sensitivity analysis of controlling parameters of SUTRENCH-model

9.1 Introduction

A detailed sensitivity analysis of th e con tro lling param ete rs of the S U T R E N C H - m odel is given by van Rijn (1984). In th is rep o rt only the influence of the m ost essential param eters, is given which are :• the flow, wave an d sedim ent tran sp o rt cond itions a t the inlet (x = 0)• the d irec tion of th e ap p ro ach in g cu rren t an d the stream line refraction effects in

the dredged channel,• the particle fall velocity of the suspended sedim ent.

These con tro lling p aram eters shou ld be based as m uch as possible on reliable and accurate m easurem ents (field survey).

9.2 Influence of hydraulic conditions at the inlet

G enerally , the inaccuracy o f the sedim ent concen tra tion profiles to be used as bo u n d ary cond itions a t the inlet (x = 0) is ra th e r large because of inadequa te

► d is tan ce (m )

uiS'

I<s

JO

2QO

21.0

22.0

23.0

24.0

25.0

26.0

-------- --------/v e s t i c b b r)o o d

------(cas .)

— M w— p ro te c te d bedT O

\ . U ' 1 >/ / È

w s = Q O ' 5 m/ S

ftJ W

I /

i J i

i &o f §

/ mV ! / ^ fc o m tx /ted bed lew2 | att< ¡r 100 days

initial bed l< 1

veljL ■ Ay ~—— norm al suspended load a t x r— . — double suspended load a t * — had suspended load a t x = 0

i j ....... _i i — i

Figure 11 Influence o f suspended load at the inlet on com pu ted bed level (tidal flow).

41

m easuring m ethods, tidal (neap-sping) a n d /o r seasonal (sum m er-w inter) fluctuations, V aria tions of a fac to r 2 a re com m only observed values. W hen detailed m easurem ents a re n o t available , the flow an d sedim ent tra n sp o rt cond itions a t the inlet (jc = 0) have to be estim ated. In th a t case the inaccuracy m ay be m uch larger th a n a factor 2.F igure 11 show s the influence o f the suspended sedim ent tra n sp o rt a t the inlet for a channel perpendicu lar to the (tidal) flow cond itions in the E astern Scheldt E stuary (The N etherlands). T he varia tion of the suspended load is assum ed to be a factor 2, As can be observed, the influence of varia tions of the suspended load on the com puted bed level profiles is ra th e r large. T he am o u n t of deposited m ateria l is alm ost linearly dependen t on the value of the incom ing suspended load.F igure 12 show s the influence of the ra tio of th e suspended (ss) and to ta l load (.s, = ss + s,,) a t the in let (x = 0). T he to ta l load is s, = 0.04 kg/sm for all three com putations. A large value of the suspended load (sjs , = 0.9) yields the largest sed im entation in the m iddle o f the channel, b u t a less rap id m ig ra tion o f the up stream side slope. These results em phasize the im portance of a correct es tim ation o f the suspended and bed load a t the inlet boundary .

> distance, x(m )

S t 0 = 0 .0 4 k g /s m hg‘ = 0 .3 9 m u0 = 0 .51 m /s

i k s = 0 .0 2 5 m I ws = 0 .0 1 3 m /s

c o m p u ta d bed level Q fter 15 h o u rs

Figure 12 Influence o f ratio o f suspended and total load on com pu ted bed level (unidirectional flow).

Finally, the influence of the w ave height on the sedim ent tra n sp o rt a t the inlet is presented. G enerally , wave p ro p ag a tio n m odels sta rtin g a t deep w ater (boundary cond itions) are used to pred ic t the local wave height, w hen local m easurem ents are no t available. D epending on the com plexity of the bed to p o g rap h y , the inaccuracy of the predicted local w ave height m ay be as la rge as 20% . F igure 13 show s the com puted bed levels for a 20% varia tion of the wave height a t the inlet. T he wave height in the channel is assum ed to be equal to th a t a t the inlet (x = 0). A change of the incom ing wave height results in a change of the incom ing sedim ent tra n sp o rt and hence a change o f the sed im entation ra te in the channel.

42

I

•QN

“OC9_D

—► distance, x (m)100 150 200 250

initial b ed level

(h0=5m, u0=1m/s, ws=0.015 m/s, ks =0.05m, T=7s)H = 2.4 m (Sb.n = 0.10 kg/smH = 2.0 m (Sb,o = 0.085 kg/smH = 1.6 m (Sb,o = 0.07 kg/sm

S,,o = 7,0 kg/sm ) S„ o = 5.0 kg/sm ) Ss,o = 3,4 kg/sm )

Figure 13 Influence o f w ave height on com pu ted bed level (unidirectional flow).

9.3 Influence of streamline refraction

T o investigate the influence of the refraction effects on the sed im en tation in a channel ob lique to the ap p ro ach in g flow, S U T R E N C H -co m p u ta tio n s were carried ou t along refracted und unrefracted stream lines. T he b o u n d ary cond itions a t the inlet w ere the sam e for all com putations. T he w ave height w as assum ed to be constan t. T h e stream line refraction was com puted num erically (see ch ap te r 8 ). F igure 14 show s the cu rren t d irection (a), the cu rren t velocity (vR), the suspended load tra n sp o r t (Ss) in teg rated over the w idth of the s tream tube , an d the bed levels for an ap p ro ach angle of a 0 = 10°. T he bed levels have been com puted for an un id irectional flow an d for a sym m etrical tida l flow. T he tidal flow is represented by tw o quasi-steady periods of 4 hours each.F irstly , the co m p u ta tio n along the refracted stream line is discussed.T he m ean cu rren t velocity a lo n g the refracted stream line show s a n increase from 1 m /s to 1.35 m /s a t the dow nstream side slope. Because of the increasing velocities the reduction of the suspended load (resulting in sed im entation), w hich is m ainly caused by co n trac tio n of the stream tube , is relatively sm all an d confined to a region upstream o f the channel axis. D ow nstream of the channel axis the suspended load tra n sp o rt increases resulting in erosion. This is clearly d em onstra ted by the com puted bed level for un id irectiona l flow show ing sed im entation up stream o f the channel axis an d erosion dow nstream of the channel axis. S im ilar p a tte rn s were observed in m odel tests carried o u t a t the H.R.S. W allingford (1973). E xperim ents w ith polystyrene particles (in suspension) in a channel w ith a rigid b o tto m show ed sed im entation upstream of the channel axis while the region dow nstream o f the channel axis rem ained free of polystyrene particles.In case of sym m etrical tida l flow the com puted bed level show s erosion in the m iddle of the ch an n el; the sed im ent m ateria l deposited du ring flood is rem oved

43

axis hn =5m

VR,0,

X charini? I

R.o 1 m/sV / refracted 0/^ stream lin e «0 '1 0

'<------------------- H = 2 munrefracted T = J. ~Lstreamline ws = 0015 m/s

ksw = 0.05 m ks'c = 0.05 m

» I K H K ■

computed alongrefracted streamline

computed alongunrcfracted streamline

a 10

0

5 0 100 5 0

m aan cu rre n t d irec tio n i a ) a t t = 0

-J_____ i i i

1.5 m ean cu rre n t velocity (vR) a t t = 0

Ë 1.0

0.5

O(/)( c ro s s - s e c t io n in te g ra te d ) suspended load (S s ) a t t = 0

j? 0,8

0.4 -

E 0bed level a f t e r 3 days (unid irectional flow )

TT

2

4

-50 50 1000— , l I 1 1 Ibed level a f t e r 10 day: ( t id a l flow )_____________Q h tN ' r

> distance

Figure 14 influence o f stream line refraction on sed im entation in a channel ob liq u e to the (low (<x0 = 10°).

44

d u rin g the eb b flow. E rosion can a lso be observed on bo th ends o f th e side slopes. Based on th e above-given co m p u ta tio n (along the refracted stream line), it seems th a t a channel inclined at an angle of 1 0 ° w ould no t on ly be self-cleansing but self- deepening as well. This is n o t credible because m an-m ade channels alw ays show sed im en tation o f m aterial. This m ust be a ttr ib u ted to secondary effects such as infill of bed-load partic les du e to the g rav ity co m ponen t causing the particles to be deflected to w ard s th e channel axis, la te ra l diffusion an d asym m etrical tida l flow. H ow ever, the overall sed im en tation rate will be ra th e r sm all because of the effect of increasing velocities in case of a sm all ap p ro a ch angle (a0 = 0 to 2 0 °),T he co m p u ta tio n a lo n g the unrefracted stream line show s a decrease o f the m ean cu rren t velocity because the cu rren t velocity is inversely p ro p o rtio n a l to the flow d ep th resu lting in a considerab le sed im en tation (Fig. 14), C om p arin g th e results for refracted an d unrefracted stream lines, it is evident th a t the refraction effect can n o t be neglected for an ap p ro a ch angle of ot0 = 1 0 °.S im ilar co m p u ta tio n s have been carried o u t for an ap p ro a ch angle of 45° and 60° (van Rijn, 1984). B ased on these results, it seems accep tab le to neglect the refraction effect for an ap p ro a ch angle betw een a 0 = 60° a n d «o = 90°,

9,4 Influence of particle fall velocity of suspended sediment

U sually , the rep resen tative partic le fall velocity is determ ined from suspended sed im ent sam ples using a (lab o ra to ry o r in -situ ) settling tube m ethod . F o r sand

-160 -80

-*■ distance (m)

O 8 0 160 240

120.0

i 21.0E

22.0<nJ.? 23.0o

Ü 24.0cih 25.0

-o260

(wI.....‘I ' ” 1est) ebb ■^>r|

■ ! — <— — > flOQtJ (ca

i

stT]i 1_ riF</̂ A/'+Arl 1

ni

bed-

M*

K J lii IJI I 1

£ iw S

\ / ,

r

<ÍS V '_„.«4 / <ij/i1V 1 8¡

I toiEL compui

""OC9 led leïvel <after

initial >ed leye 1(3ftI ------- ws =0,015m/s

— ws= 0.0185 m/si j s i i i

Figure 15 Influence o f particle fall velocity on com pu ted bed level (tidal flow).

45

particles the overall inaccuracy m ay b e as large as 25% . F o r silt particles the inaccuracy m ay be m uch larger (say 50% ), F igure 15 show s the influence of a 25% -increase of the particle fall velocity on the com puted bed level for a channel p erpend icu lar to the (tida l) flow conditions. T h e increase of the to ta l am o u n t of deposited m ateria l is a b o u t 25 %.F igure 16 show s th e influence of a 20% -increase o f the partic le fail velocity o n the com puted bed level for a channel in an un id irectional flow. A la rger partic le fall velocity yields a sm aller value of the suspended load in th e channel and hence a larger sed im entation ra te resu lting in a m ore rap id m igra tion of the upstream side slope.

distance, x(m) 6 8

initial bee

h0 = 0 .3 9 mQ0 =0.51 m /s ks = 0 .0 2 5 m CLjÿ;| co m p u ted bed level a l t e r 1 5 -h o u rs

0 .013 m /s We = 0.011 m /s

-Ö 0.20

Figure 16 Influence o f particle fall velocity o n com puted bed level (unidirectional flow).

9.5 Influence of other parameters

V aria tions (w ithin reasonab le physical ranges) o f o th e r hydrau lic pa ram ete rs such as the bed roughness, m ixing coefficients, s ta n d a rd dev iation o f the effective bed- shear stress an d the angle of in te rnal friction of the bed m ateria l particles d o n o t seriously effect the long-te rm m orpho log ical changes. This is also valid for th e type o f bed -b o u n d ary co n d itio n (bed-concen tra tion or sed im ent flux) an d th e reference level a t w hich the bed -b o u n d ary cond ition is applied (van Rijn, 1984).T he influence of w ave height varia tions (due to d ep th v aria tio n s; shoaling effect) on the sed im en tation ra te has also been investigated. T he effect on th e long -te rm m orpho log ical changes is relatively sm all an d m ay, therefore, be neglected.

46

10 Verification of SUTRENCH-model

10.1 Introduction

A com prehensive verification analysis o f the S U T R E N C H -m odel has been carried o u t for various hydraulic cond itions (van Rijn, 1984).H erein, the m ost im p o rta n t results for sed im entation in dredged channels are given. The follow ing cases are considered :

• m igration of a channel in a flume,• sed im entation in a trial d redge channel in the W estern Scheldt, T he N etherlands,• sed im en tation in a tunnel trench in a tidal river near R o tterdam , T he N etherlands,• sed im entation in a tria l d redge channel in A san Bay, K orea.

10.2 Migration of a channel in a flume

HYDRAULIC CONDITIONS

The m igration of a channel w ith steep side slopes of 1 :3 w as stud ied in a flume (length = 30 m, w id th = 0.5 m, d ep th = 0.7 m). T he sand bed w ith a thickness of 0.2 m consisted of m edium fine sand w ith a d i0 = 160 pm an d a d 9o — 200 pm. In the m easuring section a sm all channel was excavated (see F igu re 17).T o m ain ta in equ ilib rium cond itions upstream of the channel (no scour or

y

1_oN

-a<s_Q

F ig u re i 7 M ig ra tio n o f a c h an n e l in a flum e.

o > distance, x (m)4 6 8 10

OEM«S

1NI*1-

* •

\o\K>\w í f

^5_D 2vel U te r 5 hoi jrsi 1 1 c o m p u te d

* • • • m e a s u re di 1 I

9 ^ /

0.04

0.12

0.20

47

deposition), sand of the sarae size an d com position as th e bed m ateria l was supplied at a co n s tan t ra te o f 0.04 kg/sm (Delft H ydraulics L abora to ry , 1980b). T he w ater d ep th a t th e inlet w as 0.39 m. T h e cu rren t velocity at the inlet was 0.51 m/s. M easurem ents of the cu rren t velocities an d sedim ent co n cen tra tio n s upstream of the channel were used to com pute the suspended load resu lting in a value of ab o u t 0.03 kg/sm . Hence, th e bed-load tra n sp o r t w as a b o u t 0.01 kg /sm (sand feed = to ta l load = 0.04 kg/sm ).Based on the analysis o f suspended sedim ent sam ples, the rep resen tative size of the suspended sedim ent was estim ated to be 130 pm resulting in a particle fall velocity of vv.s = 0.013 m /s (tem peratu re o f 15°C). Sm all-scale bed form s w ith a height in the range 0.015 to 0.035 m an d a length in the range 0.10 to 0.25 m w ere present upstream of the channel. T he effective roughness of th e m ovable bed w as estim ated to be ks = 0.025 m (from velocity profiles).

COMPUTATIONS

T he S U T R E N C H -m odel for com plicated flows was used to com pute the m igration of the channel.At the inlet b o u n d ary (x = 0) the equilib rium concen tra tion profile (based on m easurem ents) was specified. T he velocity profile at jc = 0 was described by a logarithm ic profile. F o r these cond itions the m axim um value of the m ixing coef­ficient a t x = 0 is r.milx, o = 0.00155 m 2/s (E quation (4.5)).T he b ed -boundary cond ition was specified a t a level of a — 0,0125 m app ly ing the fi0-m ethod (E quation (5,9)). T he coefficient o f E quation (5.9) was adjusted som ew hat to give a suspended load o f ,s-4 = 0.03 kg/sm a t x = 0 (as m easured). The coefficient o f the bed-load form ula (E quation (6.5)) was also adjusted to give s b = 0.01 kg/sm a t x = 0. T he po rosity factor o f the bed m ateria l was assum ed to be 0.4. T he num erical param eters w ere: A x = 0.25 m, 10 grid po in ts in vertical direction , At = 900 s, and y s = 0.8.

RESULTS

Figure 17 shows the m igration of th e channel after 15 hours. The agreem ent betw een m easured an d com pu ted values is ra th e r good.

10,3 Sedimentation in a trial dredge channel in the Western Scheldt, The Netherlands

HYDRAULIC CONDITIONS

In 1965 a pipe line channel was dredged across the W esterschelde (W estern Scheldt), a tidal es tuary in the southw est p a rt o f the N etherlands. T he channel axis

48

w as a lm ost perpend icu lar to the flow. To estim ate the sed im en tation rate , a trial channel was dredged perpend icu lar to the tidal flow. A typical cross-section with m easured bed-level profiles is show n in F igure 18.

-200 8,25

-100-> distance (m)

0 100 200

a

£_C9o?caes£

-5Q_a-a

10.25

12.25

14.25

16.25

18 .25

20.25

'* x 1*z— K*

X X

1 bed le pril 196

& L Aß (2 6 o

<5)

e bb ■<-. . i

-> fio ad.

• • • • » m easured bed level after 22 days (18 m ay 1965) ---------------- com putedx x x x m easured bed level after 80 days (16 ju ly 1965)

------------------ com puted

Figure 18 Trial dredge channel in W estern Scheldt, T he N etherlands.

T he local hydrau lic cond itions du ring the m ean tide a re show n in F igure 19.

tidal ranae

current velocity

/ i> time (hours) lL

F ig u re 19 H y d ra u lic (tid a l) co n d itio n s .

4 9

T he bed m ateria l consisted of sand (d50 = 180 /an , d 90 = 220 pm). T he represen tative particle d iam eter of the suspendent sed im ent was estim ated to be ab o u t 140 pm resu lting in a particle fall velocity of ws = 0.015 m /s (tem perature 15ÛC). T he effective bed roughness was estim ated to be k s = 0.2 m (loca! bed-form height ~ 0 . 2 m).F low velocity an d sand co n cen tra tio n m easurem ents w ere carried ou t to determ ine the suspended load tran sp o rt.T he inaccuracy of the suspended load m ay be ra th e r large (say + 5 0 % ) because of seasonal varia tions, inaccuracy of m easuring m ethods an d system atic e rro rs (lag effects). T he bed-load tra n sp o rt w as n o t m easured.

COMPUTATIONS

T he S U T R E N C H -m o d el for com plicated flows was used to com pute the bed level profiles at various tim es. T he neap-spring tidal cycle was represen ted by the m ean tide. The m ean tidal cycle was schem atized to 4 quasi-s teady flow periods o f 2 hours each (Figure 19). T he periods w ith sm all velocities (below in itia tion of m otion) near slack tide were neglected.T o represen t the sed im ent tra n sp o rt du ring the neap-sp ring cycle correctly , the cu rren t velocities o f the m ean tida l cycle should be increased slightly (5 to 10%). In th is way th e relatively large co n trib u tio n to the sedim ent tra n sp o rt by the springtide velocities can be accounted for, as show n by V an Rijn (1984). Assum ing a pow er-law rela tionsh ip w ith an exponen t of 3 (s ~ U3) betw een the sedim ent tra n sp o rt (s) an d the m ean cu ren t velocity (u), the velocities o f the m ean tide should be m ultiplied by a fac to r 1.05. U sually , th is effect is negligibly sm all com pared w ith the inaccuracy o f the incom ing sed im ent tran sp o rt. E quilib rium concen tra tion profiles are specified a t th e inlet (x = 0). T he velocity profiles a t x = 0 are assum ed to have a logarithm ic d istribu tion . As b ed -boundary cond ition the E„-m ethod (E quation 5.9)) has been used a t a level of a = 0.1 m above the bed. T he coefficient o f E q u atio n (5.9) has been ad justed to give the co rrec t m easured suspended sand tran sp o rt a t x = 0. T h e bed-load tran sp o rt is com puted by E quation (6.5). T he po rosity factor of the bed m ateria l is assum ed to be 0.4.T he num erical param ete rs are, as follow s: A x = 5 m, 10 grid po in ts in vertical direction , At = 7200 s, ys = 0.2.

RESULTS

F igure 18 show s m easured and com puted bed levels. T he com pu ted sed im en tation rates are reasonab ly good. I t m ay be no ted th a t the m easured profiles d o n o t show erosion a t the banks.

50

10.4 Sedimentation in a tunnel trench in a tidal river near Rotterdam, The Netherlands

HYDRAULIC CONDITIONS

In 1978 a tunnel trench was dredged perpend icu lar to the flow in a sm all tidal river near R o tte rdam (B otlek-tunnel in O ude -Maas). A typical cross-section in the m iddle of the river is show n in F igure 20.

c c e»'“' £ "5 O §-t-* ™ f— L-

10

13

17

21

2 5

-120 -80 -40

- > d i s t a n c e ( m )

_0__ 40 80

<zb o < - - ! — ► f l i o dI £I

À fco m p u te d a f t e r 14 daysHSfc initial b e d level

- I I I I I "Sr

I I I

Figure 20 T unnel trench in a tidal river near Rotterdam .

T he hydrau lic cond itions are dom inated by the river flow resu lting in a d o m ina ting ebb period of ab o u t 6 hou rs (current velocity of a b o u t 0.9 m /s, w ater dep th o f a b o u t 11 m). T he effective flood period is ab o u t 4 hou rs (current velocity of ab o u t 0.6 m/s, w ater d ep th of a b o u t 10 m). T he bed consisted of fine sandy m ateria l {d50 = 200 gm , d90 = 300 gm). Based on suspended sedim ent sam ples, the represen tative particle d iam eter o f the suspended sand was estim ated to be ab o u t 110 /un resu lting in a particle fall velocity of 0.01 m /s (tem peratu re of 15°C). T he effective bed roughness was estim ated to be a b o u t 0,15 m. F low velocity and sedim ent concen tra tion m easurem ents w ere carried ou t to determ ine the suspended sedim ent tran sp o rt. T he bed load was not m easured.

COMPUTATIONS

T he S U T R E N C H -m odel for com plicated flows was used to com pute the sed im entation in the trench. T he applied b o u n d ary cond itions are sim ilar to those rep o rted in p a rag rap h 10.3. The wash o r silt load was n o t taken in to accoun t because its co n trib u tio n to the sed im entation process was assum ed to be of m inor im portance. T he num erical param eters are, as follow s: A x = 5 m, 10 grid po in ts in vertical d irection , At = 7200 s, ys = 0.05.

51

RESULTS

Figure 20 show s the com puted bed level after 14 days. T h e sed im entation in the deepest p a rt of the trench (over a length of ab o u t 25 m on bo th sides o f the axis) is abou t 25 m 3 per un it w idth. This value can be com pared w ith the m ain tenance dredging volum e of ab o u t 10 to 20 m 3 per unit w id th d u ring a period of 14 days in the sam e p art of the trench.

10.5 Sedimentation in a trial dredge channel in Asan Bay, Korea

HYDRAULIC CONDITIONS

T o o b ta in in fo rm ation of the annua l sed im entation ra te in a (planned) shipping channel in the Asan Bay of K orea, a tria l d redge channel (length of ab o u t 750 m, w idth of ab o u t 150 m, F igure 21 A) was dredged in the sum m er period o f 1983, The initial bed profile along the (refracted) stream line in the channel is show n in F igure 21 D.T o determ ine the stream line pa tte rn in the channel, a physical scale m odel (fixedbed) as welt as a m athem atical m odel was operated . Based on the m odel results,the ap p ro ach angles of the cu rren ts were found to be a 0 = 2 0 ° for the flood phase and a 0 = 15° for the ebb phase. T he cu rren t d irection in the channel was found to be a = 10° for the flood as well as the ebb phase. A nalysis o f tide d a ta show ed a sem i-diurnal type w ith a sm all d iu rn a l inequality . T he m ean tidal range is ab o u t 6

m. M axim um cu rren t velocities were in the range 0.6 to 1.2 m /s du ring the neap- spring tidal cycle.A nalysis o f wave d a ta for the sum m er period show ed a significant wave height of ab o u t 0.5 m for the flood phase and of ab o u t 0.25 for the ebb phase. The wave period was abou t 4 s.

A nalysis of various bed m ateria l sam ples show ed the presence of m edium fine sand with a m edian (d50) particle d iam eter of 200 ^m, D ata of suspended sand concen tra tions were no t available. A nalysis o f echo soundings show ed the presence of bed form s w ith a length of ab o u t 25 to 50 m, and a height o f ab o u t 0.25 to 0.50m. D etailed in form ation is repo rted by the M inistry of C o nstruc tion of theR epublic of K orea (1983).

c o m p u t a t io n s

T he S U T R E N C H -m odel for cu rren t an d waves was used to com pute the bed level changes of the tr ia l d redge channel over a period of 100 days. T he m ean tidal cycle

52

6=750 m ao=20

a 0 =15c

£S

channel axis

flood A. trial dredge channel

refracted streamlines

2 0.6 E

0.4

0

^ 0,3

B. flow v e lo c ity a t t = 0 I — f lo o di --------— e b b

c L 0 ,2 O O irt q _

s-g3 0

C. with-integrated susp. I - floodsa n d t r a n s p o r t a t t a p j — e b b

■400 •200 ±0 200 400

ec

_i(A to

0

2

4

6

8

1 0

-4 0 0 -200

channel axisI'—► distance, x (in m) 0 200 400

§■ 1 2 no

1 f 1 1 1----- >■ flood ;

— ■ -t ■ ■— i---------1---------1ebb < ------

ü0 = 0 7 8 m / s !

!uo = 0 .6 6 m / s

Iinitial b ed level I

■ a t 3 1 - 5 - 1 9 8 3 j

computed bed level (after 100 days) • • • • measured bed level D,bed level profiles along (refracted) streamline

F ig u re 21 T ria l d red g e ch an n e l in A san Bay, K orea .

53

was schem atized to 2 quasi-steady flow periods of 6 hours each. T he characteristic ap p ro ach cu rren t velocities were 0.78 m /s for the flood phase an d 0,66 m /s for the ebb phase. T he w ater dep th a t th e in let du ring flood w as ab o u t 11 m and ab o u t 6.7 m du ring ebb.Because the channel is ob lique to the ap p ro ach in g flow field, stream line refraction in the channel will occur. T he d irection of the refracted stream lines an d the m agn itude of the cu rren t velocities along the refracted stream lines were com puted by apply ing a tw o-d im ensional horizon ta l m athem atical m odel for an oblique channel of infinite length (see chap te r 8 ).T he predicted velocities were reduced slightly (10% ) to acco u n t for the finite length of the trial d redge channel. T he S U T R E N C H -m odel was applied along a refracted stream line. T he cu rren t velocities were represented by varying the w idth of the flow (stream tube app roach ). T he com puted cu rren t velocities, presented in F igure 21B, show a sm all increase of the velocities in the channel.At the inlet b o u n d ary (x = 0) equ ilib rium co n cen tra tio n profiles w ere specified. S tandard coefficients were used. D a ta for ca lib ra tio n were n o t available. T he represen tative particle d iam eter o f the suspended sand m ateria l was estim ated to be ab o u t 150 pm resu lting in a fall velocity of a b u t ws = 0.016 m /s (Te ~ 20° C).As bed -boundary cond ition the E„-m ethod was used, applied a t a level of 0.15 m above the m ean bed. The effective roughness was assum ed to be = 0.15 m.T he bed-load tra n sp o rt was com puted by E quation (6.4).S edim entation of bed-load particles by gravity infill from the side slopes was neglected.T he num erical param ete rs a re : A x = 25 m, 10 grid po in ts in vertical d irection , At = 21600 s, y, = 0.1.

RESULTS

F igure 21C show s the w id th -in teg ra ted suspended sand tra n sp o r t (at t = 0) for the flood an d ebb phase of the tide. T he flood phase is the d o m in a n t period for the sedim ent tran sp o rt. F igure 21D show s m easured an d com puted bed levels after a period of 100 days. T he agreem ent is ra th e r good, particu larly a t the banks of the channel w here erosion can be observed. In the m iddle o f the channel there is also a sm all region w ith erosion , p robab ly caused by relatively large cu rren t velocities. This effect was n o t predicted by the S U T R E N C H -m odel. T he reason for th is m ay be an underprodiction of the cu rren t velocities in the channel.

54

11 Sediment trapping efficiency of dredged channels and trenches

11.1 Introduction

T o o b ta in sim ple rules for sed im en tation p red ic tions, the S U T R E N C H -m o d el has been applied to determ ine the trap p in g efficiency of dredged channels w ith various d im ensions an d ap p ro a ch angles, as show n schem atically in F igure 22. T he channel is assum ed to be infinitely long (along th e axis). S tream line refraction in the channel has been com p u ted num erically , as p resented in ch ap te r 8 , resu lting in the m agn itude an d direction of the cu rren t velocity vector a t each location . These

channel axis

^unit channel length

*

Figure 22 D efin ition sketch for sed im ent trapp ing efficiency o f dredged channels.

55

results have been specified to the S U T R E N C H -m odel (stream tube approach). Based on this, the S U T R E N C H -m odel com putes the suspended sedim ent tran sp o rt a long the stream tube.

11.2 Computations

In all, 300 co m p u ta tio n s have been executed using the follow ing d a ta (see also F igure 22):

ap p ro ach cu rren t velocity : Vr ,o = 1 m /sap p ro ach w ater dep th : h0 = 5 map p ro ach angles : x 0 = 15°, 30°, 60° an d 90°channel dep th d = 2, 2.5, 5 an d 10 mchannel w idth (norm al to axis) :b = 50, 100, 200 an d 500 mchannel side slope (norm al to axis) : ta n y = 1 :5 , 1 :1 0 and 1 :20partic le fall velocity : ws = 0.0021, 0.005, 0.0107, 0.0142

0,025 and 0.036effective bed roughness ■ks = 0 . 2 m

11.3 Results

T he trap p in g efficiency (e) is defined as the relative difference of th e incom ing suspended sedim ent tra n sp o rt an d the m inim um value of the suspended sedim ent tra n sp o rt in the channel :

bo so — (hi Sie = — .................... ( 1 . 1 1 )

b0 s0in which :

b0 = ap p ro a ch w id th of stream tube (m)b { = w id th of stream tube in channel (m)s 0 — incom ing suspended sedim ent tra n sp o rt per unit w idth (kg/sm )s t = suspended sedim ent tra n sp o rt p er un it w idth in channel (kg/sm )

T he basic param ete rs w hich determ ine the trapp ing efficiency are : the ap p ro ach angle (ot0)! ap p ro a ch velocity (ür,o) an d d ep th (f?0), ap p ro ach bed-shear velocity (u,*,0 ), partic le fall velocity (ws), channel d ep th (d), channel w idth (b) an d channel side slope (tan 7 ).T he functional re la tionsh ip is :

r, l - wv d be = F(«a, Ufi.o, , — , -p-, ta n y ) (1 1 ,2 )

« * , 0 ho h0

56

F igu re 23 presen ts the resu lts for a channel perpend icu lar (a0 = 90°) to the flow direction . These results show th a t the influence of the side slope angle (y) is negligibly small.

&C

’u

oc

p♦

1.0

0 ,8

0.6

0.4

0.2

0

: 0 .4 ta n it = 1.5

^ = 0 .U*,o 5 Í 3 . -

es. 5Q ^q ^ S -

o.oT—

0.03

O 30 60 90 120

tan 6 =1:2Ca 0 = 9 0

30 60 90 120

t a n i i = 1:20

1.0

0.8

0.6

0.4

0.2

30 60 90 120

t a n i f = 1:5

0,8

0.6

ol 0.4

0.2

30 60 90 120

5>C

<J£ÍSUiÇ'cuCUau

Î

ton ïf -1 5a 0 * 9 0

channel w idth, ru

tanX =1:20ao =90

90 120channel width, P -

Figure 23 Sedim ent trapping efficiency o f a channel perpendicular to the flow (a0 = 90°).

57

A dditional results for ob lique channels are given by van Rijn (1984).The sed im en tation ra te (in kg/sm ) per un it channel leng th (along the axis) im m ediately after dredging can be com puted by (see F igure 22):

D = e s 0 sin a 0 (11.3)

Finally, it is no ted th a t this sim ple ap p ro a ch only yields a rough estim ate of the sed im entation rate , w hich should not be used for detailed feasibility and econom ical studies o f sh ipping channels.

58

12 References

A l f r i n k , B.J. and R i jn , L.C. van, 1983, T w o-E q u ation T urbulence M odel for F low in Trenches, Journal o f H ydraulics D iv ision , A SC E , vol. 109, N o . 3, U SA .

B o e r , S„ 1984, T he F low across T renches a t O blique A ngle to the F low , D elft H ydraulics Laboratory, R eport S490, D elft, T he N etherlands.

C o le m a n , N .L ., 1970, F lum e Studies o f the Sedim ent Transfer C oefficient, W ater R esources Research, Vol. 6, N o . 3, U SA .

C o l e s , D ., 1965, T he L aw o f the W ake in the T urbulent B oundary Layer, Journal o f Fluid M echanics, Vol. I, E ngland.

D f . l f t H y d r a u l i c s L a b o r a t o r y , 1975, Sedim entation o f T unnel T renches ( in D u tch ), R ep ort R 975-I ,

D elft, T he N etherlands.D e l f t H y d r a u l i c s L a b o r a t o r y , 1977, N um erical M od el for N on-Steady Suspended Sedim ent T ransport

R eport R 9 7 5 -II , D e lft, T he N etherlands.D e l f t H y d r a u l i c s L a b o r a t o r y , 1980b, C om pu tation o f S ilta tion in D red ged T renches, R eport

R eport R 1267—III, D elft, T he N etherlands.D e l f t H y d r a u l i c s L a b o r a t o r y , 19S0b, C om pu tation o f S iltation in D red ged T renches, Report

R 1 2 6 7 -V , D elft, The N etherlands.D e l f t H y d r a u l i c s L a b o r a t o r y , 1981a, Entrainm cnt o f F in e Sed im en t Particles; D eterm ination o f

Bcd-shear V elocities, R eport M 1531-L D elft, T he N etherlands.D e l f t H y d r a u l i c s L a b o r a t o r y , 1 9 8 1 b , E ntrainm ent o f F ine Sedim ent Particles; D evelop m ent o f

C oncentration Profiles in a Steady U niform F lo w w ith ou t Initial Sedim ent L oad, R e p o r t M 1531 -1 1 , D elft, T he N etherlands.

D e l f t H y d r a u l i c s L a b o r a t o r y , 1983a, Entrainm ent o f F ine Sedim ent Particles; In itiation o f M otion and Suspension , D evelop m en t o f C oncentration Profiles in a Steady U niform F lo w w ith out Initial Sedim ent L oad , R eport M 1531-111, D elft, T he N etherlands.

D e l f t H y d r a u l i c s L a b o r a t o r y , 1 9 8 3 b , Entrainm ent o f Fine Sedim ent Particles; Sedim ent Pick-up F u nctions, R eport M 1531-IV , D e lft, T he N etherlands.

H j e l m f e l t , A .T . and L e n a u , C .W ., 1970, N on-E quilibrium T ransport o f Suspended Sedim ent, Journal o f the H ydraulics D iv ision , A SC E , H Y 7, U SA .

H .R.s. W a l l i n g f o r d , 1973 , Laboratory Studies o f F low across D redged C hannels, R eport E X 6 1 8 , W allingford, England.

K e r s s e n s , P .J.M ., 1977, M orphological C om pu tation s for Suspended Sedim ent T ransport, D elft H ydraulics Laboratory, R eport S 7 8 -V I, T he N etherlands.

K e r s s e n s , P.J.M ., P r i n s , A . and R i j n , L.C, van, 1979, M odel for Suspended Sedim ent Transport Journal o f the H ydraulics D iv is io n , A S C E , H Y 5 , U S A .

K e r s s e n s , P.J.M . and R i j n , L.C. van, 1977, M odel for N on -S tead y Suspended Sedim ent T ransport 18th lA H R -con gress , B aden-B aden, W est-G erm any.

R e p u b l i c o f K o r f .a , M inistry o f C onstruction , 1983, Sedim entation S tudy for N av iga tion C hannel o f the P yeong T eak L N G R eceiving T erm inal, V olum e I.

R o n i, W ., 1980, T urbulence M odels and their A pplication in H ydraulics, IA H R -section on F undam entals o f D iv is ion II, D elft, T he N etherlands.

R u n , L .C . van, 1980, M odel for Sed im en tation Predictions, 19th lA H R -con gress , N ew D elh i, India.R i j n , L.C, van , 1981, C om p u tation o f B ed-load C oncentration and Bed L oad T ran sp ort, D elft

H ydraulics Laboratory, R eport, S 4 8 7 -L D e lft, T he N etherlands.R u n , L .C . van, 1982a, C om pu tation o f Bed L oad and Suspended L oad Transport, D elft H ydraulics

L aboratory, R eport, S 4 8 7 -II , D elft, The N etherlands,R ijn, L .C . van, 1982b, Prediction o f Bed Form s, A lluvial R oughness and Sedim ent T ransport, D elft

H ydraulic L aboratory, R eport, S 4 8 7 -IH , D elft, T he N etherlands.

59

R i jn , L.C. van, 1983, T w o-D im en sion al M athem atical F low M ode! w ith a T w o-E q u ation T urbulence C losure, D elft H ydraulics Laboratory, Report S 4 8 8 --I, D elft, T he N etherlands,

R i jn , L.C. van, 1984, T w o-d im en sion al Vertical M athem atical M odelling o f Suspended Sedim ent by Current and W aves, D elft H ydraulics L aboratory, R eport S 488-1V , D elft, T he N etherlands.

R ijn , L.C. van, 1985, Initiation o f M otion, Bed F orm s, Bed R oughn ess, Sedim ent C oncentration and T ransport by Current and W aves, D elft H ydraulics Laboratory, R eport S 487-IV , D elft, T he N etherlands.

VitEUODKNJJlL, C ,B „ 1982, N um erical Solu tion o f a C on vection -D iffu sion E quation using F inite E lem ents D elft H ydraulics Laboratory, Internal N o te X 59, D elft, T he N etherlands.

60

In the series of R ijksw aterstaat C om m unications th e follow ing num bers have been previously published:

N o . I.

N o . 2.

N o . 3.

N o . 4.

N o . 5.

N o , 6.

N o , 7.

N o . 8,

N o , 9,

N o , 10.

N o , 11.

N o . 12,

N o . 13.

N o , 14.

N o . 15.

N o . 16,

N o . 17.

T id a l C om puta tions in Sha llow W ater D r. J, J, D ronkers f and prof, dr. ir. J. C. Schönfcld R eport on H ydrosta tic Leveling across th e W eslerschelde Ir. A . W aalew ijn, 1959

C om puta tions o f the D ecca P a tien t fo r the N etherlands D elta W orks Ir. H. Ph, van der Schaaf f and P. V etterli, Ing. D ip l. E. T. H ., 1960

T h e A g in g o f A spha ltic B itum enIr. A . J. P. van der Burgh, J. P. B ouw m an and G . M . H . Steffelaar, 1962

M u d D istribution a n d L a n d R eclam ation in th e E astern W adden Shallow s D r. L, F. K am ps t , 1962

M odern C onstruction o f W ing-G aies Ir, J. C. le N o b e l, 1964

A S tructu re P lan fo r th e So u th ern IJsselm eerpolders Board o f the Z uyder Zee W orks, 1964

T h e Use o f E xp losives fo r C learing le e Ir. I. van der K ley , 1965

T h e D esign a n d C onstruction o f th e Van B n en en o o rd B ridge across the R iver N ieu w e M aas Ir. W . J. van der Eb f , 1968

Electronic C om puta tion o f W a ter Levels in R ivers d u rin g H igh D ischarges Section R iver Studies. D irectie B ovenrivicren o f R ijksw aterstaat, 1969

T h e C analiza tion o f th e L ow er R h ineIr. A , C, de G aay and ir, P. B lokland f , 1970

T h e H aringvliet Slu icesIr. H. A . Ferguson, ir. P. B lokland f and ir. drs. H . K uiper, 1970

T h e A pp lica tion o f P iecew ise P o lynom ina ls to P roblem s o f C urve a n d S u rfa ce A p p ro x im a tio n D r. K urt K ubik, 1971

S y s te m s fo r A u to m a tic C om puta tion a n d P lo tting o f Position P atterns Ir. H. Ph. van der S c h a a ft , 1972

T h e R ea liza tion a n d F unction o f the N orthern B asin o f the D elta Project D eltad ien st o f R ijksw aterstaat, 1973

F ysica l-E ngineering M o d e l o f R ein fo rced C oncrete F ram es in C om pression Ir. J, B laauw endraad, 1973

N aviga tion L o ck s f o r P ush Tow s Ir. C. K oom an , 1973

P n eu m a tic B arriers to reduce S a lt In trusion through L o cks D r. ir. G . A braham , ir. P, van der Burg and ir. P . de V os, 1973

61

N o . ! 8. E xperiences w ith M a th em a tica l M odels used fo r W ater Q uality a n d W ater Problem s Ir, J, V o o g t and dr, ir, C , B. V reugdenhil, 1974

N o , 19.

N o. 20.

N o . 21.

N o . 22.

N o. 23.

N o. 24.

N o. 25.

N o. 26.

N o . 27.

N o . 28.

N o. 29

N o. 30.

N o 31

N o . 32.

N o . 33.

N o . 34.

N o . 35.

S a n d S ta b iliza tio n a n d D une B uild ingDr. M. J. A driani and dr. J. H . J. Terw indt, 1974

T he R oad-P ic tu re as a Touchstone fo r th e three d im ensiona l D esign o f Roads Ir. J. F, Springer and ir. K . E. H uizin ga (also in G erm an), 1975

P ush Tow s in Canals Ir. J. K oster, 1975

L o c k C apacity a n d T ra ffic R esistance o f L ocks Ir. C. K oom an and P. A . de Bruijn, 1975

C om pu ter C alculations o f a C o m p lex S tee l B ridge verified by M odeI Investiga tions Ir. Th, H. K ayser and ir J, Brinkhorst, 1975

T h e K reekra k L o cks on the Sch e ld t-R h in e C onnection Ir. P. A. K olk m an and ir. J. C. Slagter, 1976

M otorw ay T unnels bu ilt bij th e Im m ersed Tube M eth o dIr. A . G lerum , ir B. P. R igter, ir. W. D . Eysink and W. F. H eins, 1976

S a lt D istribu tion in EstuariesR ijksw aterstaat, D e lft U n iversity o f T echn ology, D e lft H ydraulics L aboratory, 1976

A sp h a lt R e ve tm en t o f D y k e SlopesC om m ittee on the C om paction o f A sp h alt R evetm ents o f D yke Slopers, 1977

C alculation M ethods fo r T w o-d im ensiona l G roundw ater f lo w Dr. ir. P. van der Veer, 1978

Ten yea rs o f Q u a lity C on tro l in R o a d C onstruction in the N etherlands Ir, C . van de Fliert and ir, H . Schram , 1979

D ig ita l L arge S ca le R estitu tio n a n d M ap C om pila tionJ, G . van der K raan, H . R ietveld , M . T ienstra and W . J. H . H zereef, 1980

P olicy A n a lys is fo r the N a tio n a l W a ter M a n a g em en t o f th e N etherlands(N etherland s C ontributions, related to the P A W N -stu dy , for the E C E-sem inar o n E conom icInstrum ents for the R ation a l U tilization o f W ater R eso u rces-V e ld h o v en , N e th e r la n d s - 1980)

C hanging Estuaries Dr, H , L. F , Saeijs, 1982

A B ird ’s E ye View o f lile Shipp ing T ra ffic on the N orth S eu N orth sea directorate, 1982

C ontributions to R em o te Sensing: A pp lica tions o f T h erm a l In fra redH. W. Brunsveld van H u lten (ed.), P. H oogen b oom , A . F. G. Jacobs, C. K raan, G. P. de L oor and L. W artena, 1984

O n the C onstuction o f C om puta tiona l M ethods fo r Sha llow W ater Flow Problem s D r. ir, G . S. Stelling, 1984

62

N o , 36, W rong-w ay driving Ir. G . A . Brevoorti

N o , 37, The Use o f A sp h a lt in H ydrau lic E ng ineeringT echnical A dvisory C om m ittee o n W aterdefences, 1985

N o . 38, R ecycling o f R o a d P avem en t M ateria ls in the N etherlands J. J. G erardu and C. F . H endriks, 1985

N o . 39, G roundw ater In filtra tio n w ith B ored W ellsN ation a l Institute for W ater Supply, et al, 1985

N o , 40. B iological Research E m s-D oU ard E stuaryB io log ica l Study o f the E m s-D ollard Estuary (B O E D E ), 1985