11

Geometric and migrating characteristics Geometric and migrating characteristics of superimposed bedforms under of superimposed bedforms under

oscillatory flowsoscillatory flows

Ven Te Chow Hydrosystems Laboratory Department of Civil and Environmental Engineering

University of Illinois at Urbana-Champaign2005

ByYovanni Cataño

And Marcelo H. García

22

Outline

AcknowledgementsAcknowledgements MotivationMotivation Experimental setupExperimental setup Formation of superposed bedforms under Formation of superposed bedforms under

oscillatory flowsoscillatory flows Main results: (a) SandwavesMain results: (a) Sandwaves

(b) Ripples(b) Ripples ConclusionsConclusions Future workFuture work

33

AcknowledgementsAcknowledgements

Coastal Geosciences Program of the Coastal Geosciences Program of the U.S. Office of Naval Research Grant: U.S. Office of Naval Research Grant: N00014-05-1-0083 N00014-05-1-0083

Prof. James Best University of Leeds Prof. James Best University of Leeds (UK)(UK)

Prof. David Admiral University of Prof. David Admiral University of NebraskaNebraska

44

MotivationMotivation Understanding formation and evolution of coexisting

bedforms under combined flows

Important for the interaction of bedforms with coastal structures: pipelines, cables, cylinders, bridge piers, breakwaters…

Other applications include the exploitation of sands for construction purposes

Implications on effective roughness height induced by bedforms.

55

Experimental setupExperimental setup

49 m

1.8 m 1.8 m1.2 m 6.2 m 0.9 m 1.8 m 24 m

0.31 m

1.20

m

2

3

1112 13

5

8

9

10

7

1

4

zx y

4 6

1. wave flume; 2. wavemaker paddle; 3. injection of current; 4. wooden ramp; 5. waves; 6. Seatek sensors; 7. superimposed current; 8. sandy bed; 9. beach; 10. sediment trap; 11. movable carriage; 12. water surface acoustic sensor; 13. ADV probe.

66

Bedform formation and evolution

77

Bed configuration with the presence of 2D and 3D ripples. Hydraulic conditions: Tw = 3.4 s, Hw =

10.7 cm, Lw = 7.7 m. Horizontal and transverse resolutions are 1 cm, and 4 cms, respectively.

Amalgamated bedforms

Survey with the Seatek sensors

88

Typical view of ripples superimposed on a sandwave under WA. Typical view of ripples superimposed on a sandwave under WA.

99

Measured dimensionless sandwave height as a function of the Reynolds wave number.

Measured dimensionless sandwave length as a function of the Reynolds wave number.

h sw /a = 175.76R ew-0.54

ρ 2 = 0.34

0.01

0.1

1

10

10000 100000 1000000R ew

h sw /

a

Present study, WA

Present study, CF

Power (Presentstudy, WA)

l sw /a = 10024R ew-0.56

ρ 2 = 0.651

10

100

1000

10000 100000 1000000R ew

l sw /

a

Present study, WA

Present study, CF

Power (Present study,WA)

Results: sandwaves

1010

0.1

1

10

10000 100000 1000000

R ew

L sw

/ L

w

Present study, WA

Present study, CF

L sw / L w = 0.44

Dimensionless sandwave length as a function of the Reynolds wave number

0.001

0.01

0.1

1

10

10000 100000 1000000

R ew

Vgr

(cm

/hr)

WA, present study

CF, present study

Measured sandwave vertical growth rate as a function of the Reynolds wave number.

harmonics

1111

Evolution over time of a measured bed profile

1212

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 to 0.5 0.5 to 1 1 to 1.5 1.5 to 2 2 to 3 3 to 4 4 to 6 6 to 26 26 to 50Interval (hours)

Vgr

(cm

/hou

r)

Vertical growth rate of sandwave as a function of time. Case of waves alone.

1313

Measured dimensionless sandwave migration speed as a function of the Reynolds wave number.

0.000001

0.00001

0.0001

10000 100000 1000000R ew

Csw

/ U

wc

Present study, WAPresent study, CF

1414

Main findings: Sandwave formation and evolution

•Sandwave geometry parameters such as height, length, and steepness show less scatter, although considerable, when plotted against Rew than for the case of ψwc or θ.

•Both sandwave length and height decrease as the Reynolds wave number increases

•Dimensionless sandwave migration speed increases as the Reynolds wave number increases.

•Preliminary analysis suggest the existence of a simple relationship between the sandwave length (Lsw) and wavelength of the surface wave (Lw)

Experiments for: 10 < ψwc < 88; 16000 < Rew < 500000, and 0.09 < θ < 0.54

For flat bed conditions

1515

Results:Results: Ripples superimposed to Ripples superimposed to sandwavessandwaves

0.1

1

10

10000 100000 1000000R ew

l r /

a

Measured, WAPredicted by Eq. 6.7, WAMeasured, CFPredicted by Eq.6. 7, CF

Dimensionless mean ripple wave length as a function of the Reynolds wave number defined as Rew = Uwc a / ν. With ψwc

0.0001

0.001

0.01

0.1

1

10000 100000 1000000R ew

h r

/ a

Measured, WAPredicted by Eq. 6.10, WAMeasured, CFPredicted by Eq. 6.10, CF

Dimensionless mean ripple wave height as a function of the Reynolds wave number defined as Rew = Uwc a / ν. With ψwc

GeometryRipples over crest

1616

0

1

2

3

4

5

6

7

Flat bed Over Crest Between crest andtrough

Trough

Cr

(m/d

ay)

Variation of ripple speed depending on its relative position over the sandwave under waves alone.

Ripple speed

1717

Measured velocity profiles after 34 hrs. ΔX = 25.4 cm.

Smaller asymmetry

Larger asymmetry

1818

Mean value of measured dimensionless ripple speed as a function of the mobility number.

Cr/Uwc = 0.0002Ln(ψwc) - 0.0007

R2 = 0.78

Cr/Uwc = 0.0002Ln(ψwc) - 0.0003

R2 = 0.41

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

1 10 100ψ wc

Cr / U

wc

Present study, WA

Present study, CF

Faraci & Foti (2002), RegularwavesFaraci & Foti (2002), Randomwaves

1919

Main findingsMain findings

Ripples size, shape and speed vary depending on their relative position over the sandwave.

Measured ripple length and height show strong dependency on the Reynolds wave number Rew for WA and CF.

10 < ψwc < 88 and 16000 < Rew < 500000, and 0.09 < θ < 0.54

For flat bed conditions

2020

Thank you!Thank you!

Any questions?Any questions?

2121

•Since the ripple washout mechanism continues to be unclear, it is proposed to reproduce higher values of the mobility number similar to those observed in the field.

• Since bedforms are subjected to irregular flows in the field, it is easy to understand the urgent need to conduct laboratory experiments with the combination of irregular waves and currents.

•Perform measurements of sediment concentration profiles along sandwave.

Signal Analysis of Time Series and Bottom Records • To explore convenience of using Hilbert and wavelet techniques along of FFT, and

Spectral Analysis

Predictive tools• It is proposed to explore the use of analytical approaches, such as stability analysis and

weakly non-linear theory, Mei theory.

Proposed experimental work (continuation)

2222

Shortcomings & Shortcomings & RecommendationsRecommendations

Use of linear small wave theory (Rigorously: Cnoidal, 2Use of linear small wave theory (Rigorously: Cnoidal, 2ndnd order Stoke’s theory) order Stoke’s theory)

Include in the calculations of Include in the calculations of θ the effect of form drag due to ripples and θ the effect of form drag due to ripples and sandwaves.sandwaves.

Non-linearity due to beach reflection, and wavemaker?Non-linearity due to beach reflection, and wavemaker?

So far, work with So far, work with UUcc < 20 cm/s < 20 cm/s

Due to a changing bed (Ripples and sandwaves), only mean velocity are suitable Due to a changing bed (Ripples and sandwaves), only mean velocity are suitable for description of global processes.for description of global processes.

No turbulence characterization over ripples and sandwaves.No turbulence characterization over ripples and sandwaves.

Better to use of PIV (Particle Image Velocimetry) or ADVP techniques (Acoustic Better to use of PIV (Particle Image Velocimetry) or ADVP techniques (Acoustic Doppler Velocimeter Profiler)-> Doppler Velocimeter Profiler)-> resolve turbulence, others….resolve turbulence, others….

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Additional work would include:Additional work would include:

To perform refined velocity measurements over an To perform refined velocity measurements over an artificial fixed sandwave (If ADV is the artificial fixed sandwave (If ADV is the only instrument available)only instrument available). .

--Examine Reynolds stresses distribution and momentum fluxesExamine Reynolds stresses distribution and momentum fluxes over three and two over three and two dimensional ripples superimposed on sandwaves. dimensional ripples superimposed on sandwaves.

- Estimation of the distribution of the friction factor - Estimation of the distribution of the friction factor ffww, and roughness length , and roughness length zzoo, over the , over the bedforms.bedforms.

- The implications for sediment transport characteristics would also be understood.- The implications for sediment transport characteristics would also be understood. - Will help future development of numerical and analytical models dealing with the - Will help future development of numerical and analytical models dealing with the

morphodynamics of the studied bedforms.morphodynamics of the studied bedforms.

With movable bedWith movable bed: The effects due to ripples and sandwaves must be separated to obtain a : The effects due to ripples and sandwaves must be separated to obtain a better description of the hydrodynamic processes over the whole flow field. better description of the hydrodynamic processes over the whole flow field. ADV not suitableADV not suitable. . It is better to use It is better to use PIVPIV (Particle Image Velocimetry) or (Particle Image Velocimetry) or ADVPADVP (Acoustic Doppler Velocity (Acoustic Doppler Velocity Profiler) techniques where spatial and temporal resolution can be significantly improved. Profiler) techniques where spatial and temporal resolution can be significantly improved.

Since bedforms are subjected to Since bedforms are subjected to irregular flowsirregular flows in the field, it is easy to understand the urgent in the field, it is easy to understand the urgent need to conduct laboratory experiments with the combination of irregular waves and currents.need to conduct laboratory experiments with the combination of irregular waves and currents.

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ReferencesReferences Cataño-Lopera, Y. and García, M.H., (2005e). “Geometry and Migration Characteristics of Bedforms under

Waves and Currents: Part 1, Sandwave morphodynamics.” Submitted to Coastal Engineering.

Cataño-Lopera, Y. and García, M.H., (2005f). “Geometry and Migration Characteristics of Bedforms under Waves and Currents: Part 2, Ripples Superimposed on Sandwaves.” Submitted to Coastal Engineering.

Cataño-Lopera, Y. and García, M.H., (2005g). "Geometric and migrating Characteristics of Amalgamated Bedforms under Oscillatory Flows." Proceedings of the 4th IAHR Symposium on River, Coastal and

Estuarine Morphodynamics, University of Illinois, October 4-7.

Faraci, C. and Foti, E., (2002). “Geometry, migration and evolution of small-scale bedforms generated by regular and irregular waves.” Coastal Engineering, 47, 35-52.

Williams, J.J., Bell , P.S. and Thorne, P.D., (2005). “Unifying large and small wave-generated ripples.” J. Geophys. Res., 110 (CO2008).

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mw

fm Uf

U2

dg

U

s

fm

)1(

2

Go back

d = fluid orbital diameter

a

Shear velocity

Shields parameter

50

2

1 gds

Umw Mobility number

aU

RE m Reynolds wave number

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0

5

10

15

20

25

30

35

40

45

0 500 1000 1500 2000 2500

2727

Laser image of a sharp boundary between Laser image of a sharp boundary between sand wavessand waves ( (top left cornertop left corner) and ) and smooth seafloorsmooth seafloor. .

Influence of development and migration of bedforms on the burial process

Type of bedformsType of bedforms Typical lengthTypical lengthLL

Typical heightTypical heightHH

Length/height ratioLength/height ratio

RipplesRipples 0.04 – 0.6 m0.04 – 0.6 m0.003 – 0.06 m0.003 – 0.06 m 8 – 158 – 15

Mega ripplesMega ripples 0.6 – 30 m0.6 – 30 m0.06 – 1.5 m0.06 – 1.5 m > 15> 15

SandwavesSandwaves 30 – 1000 m30 – 1000 m 1.5 – 15 m1.5 – 15 m > 30> 30

Bedform Bedform typetype

(sandy bed)(sandy bed)Related flowRelated flow

WavelengthWavelengthLL (m) (m)

Amplitude Amplitude AA (m) (m)

Time scale Time scale TT

Migration Migration rate rate CC

RipplesRipples Instant flowInstant flow ~ 1~ 1 ~ 0.01~ 0.01 hrshrs ~ 1 m/day~ 1 m/day

Mega-Mega-ripplesripples

Storm, surgesStorm, surges ~ 10~ 10 ~ 0.1~ 0.1 DaysDays~ 100 ~ 100

m/yem/yearar

SandwavesSandwaves TideTide ~ 500~ 500 ~ 5~ 5 YearsYears~ 10 ~ 10

m/yem/yearar

Long bed Long bed waveswaves

UnknownUnknown ~ 1500~ 1500 ~ 5~ 5 UnknownUnknown UnknownUnknown

Tidal Tidal sandbsandbanksanks

TideTide ~ 5000~ 5000 ~ 10~ 10 CenturyCentury ~ 1 m/year~ 1 m/year

Table 1. Ref. Reineck, H.-E, Singh, I.B., and Wunderlich, F., 1971.

Table 2. Ref. Characteristics of offshore sand bedforms, Morelissen, R., et al. Coastal Engineering (2003), 197-209

2828

Also…..

Other contributors: ONR program: Theoretical and field: Gallagher et al. (1998) Theoretical and Laboratory: C. C. Mei, MIT (2002)

Theoretical (Stability analysis), numerical modeling, and field of sandwaves: Amos, Németh, Komarova, Holsters, Gekerma, others....

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0.1

1

10

1 10 100 1000ψwc

l r /

a

Regular waves, (Faraci & Foti, 2001)Irregular waves, (Faraci & Foti, 2001)Lab. data (Nielsen, 1981)Field data (Nielsen, 1981)Waves alone (Khelifa & Ouellet, 2000)Combined flow (Khelifa & Ouellet, 2000)Lab. data, CF (Khelifa & Ouellet, 2000)Present study, WAPresent study, CF

Dimensionless ripple length as a function of the mobility number under waves alone and combined flow.

Back

3030

0.01

0.1

1

1 10 100 1000ψwc

h r

/ aRegular waves, (Faraci & Foti, 2001)Irregular waves, (Faraci & Foti, 2001)Lab. data (Nielsen, 1981)Field data (Nielsen, 1981)Waves alone (Khelifa & Ouellet, 2000)Combined flow (Khelifa & Ouellet, 2000)Lab. data, CF (Khelifa & Ouellet, 2000)Present study, WAPresent study, CF

Dimensionless ripple height as a function of the mobility number under waves alone and combined flow.

Back

3131

Experimental InstrumentationExperimental Instrumentation

ADV (SonTek) for 3D velocity profiles and sinking of the mine

Acoustic sensor (STI) for measurement of time series of water surface profile

A 32 composite element array of sub-aquatic acoustic sensors (SeaTek - Multiple Transducer Arrays) for

3D mapping of the bottom

BackBack

3232

Velocity profiles recorded after 34 hours. The duration of each velocity point was 180 s covering more than 60 wave periods. Vertical velocity profiles are spaced every 25.4 cm in the x-direction over the centerline of the flume. Hydraulic conditions: Tw = 4.1 s, Lw = 9.4 m, Hw = 10.4 cm, h = 56 cm under waves alone.

3333

Contour map of the sandy bottom and velocity vectors over the centerline of the center sandwave. Flow conditions for waves alone: Tw = 2.3 s, Lw = 4.9 m, Hw = 17.4 cm, h = 60 cm. Average values

of morphodynamic characteristics, for ripples: length, lr = 12.7 cm, height, hr = 1.5 cm and speed,

cr = 8.4 cm/day; for sandwave: length, lsw = 8.4 m, height, hsw = 40 cm and speed, csw = 95 m/year.

Up to date only two experiments include this type of velocity measurements.

Velocity measurements

back

3434

Go back

3535

Go back to recommendations

Go back to theoretical background

3636Go back

Support

3737

-4

-3

-2

-1

0

1

2

3

4

5

6

0 2 4 6 8 10Time (s)

η (c

m)

-6

-4

-2

0

2

4

6

0 5 10 15 20

Time (s)

η (

cm)

Examples of surface profiles (case of waves alone) for: (Left) Quasi-sinusoidal wave type with Tw = 1.5 s, Lw = 3.0 m, Hw = 7.1 cm, Cw = 2.1 m/s, Stroke=6.1 cm. (Right) Stokes’ wave type with Tw = 2.9 s, Lw = 6.6 m, Hw = 8.7 cm, Cw = 2.1 m/s, Stroke=15.2 cm. Notice that η = 0 cm corresponds to the undisturbed water level of h = 56 cm

3838

Ratio between measured data and predicted values as a function of the Reynolds wave number, Re: (a)

Sandwave length, (b) Sandwave migration speed.

220

klsw

2

2

10

m

isw T

C

Theoretical, Németh et al. (2002) (agree with field data) …but not present study!

Tm = (Time scale) ??

10

100

1000

10000 100000 1000000R ew

Lsw

mea

sure

d /

Lsw

pre

dic

ted

Present study, WA

Present study, CF

(a)

1

10

100

1000

10000 100000 1000000R ew

Csw

mea

sure

d / C

sw p

redi

cted

Present study, WA

Present study, CF

(b)