1 Geometric and migrating characteristics of superimposed bedforms under oscillatory flows Ven Te Chow Hydrosystems Laboratory Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign 2005 By Yovanni Cataño And Marcelo H. García

2 Outline Acknowledgements Acknowledgements Motivation Motivation Experimental setup Experimental setup Formation of superposed bedforms under oscillatory flows Formation of superposed bedforms under oscillatory flows Main results: (a) Sandwaves Main results: (a) Sandwaves (b) Ripples Conclusions Conclusions Future work Future work

3 Acknowledgements Coastal Geosciences Program of the U.S. Office of Naval Research Grant: N Coastal Geosciences Program of the U.S. Office of Naval Research Grant: N Prof. James Best University of Leeds (UK) Prof. James Best University of Leeds (UK) Prof. David Admiral University of Nebraska Prof. David Admiral University of Nebraska

4 Motivation 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.

5 Experimental setup 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.water surface acoustic sensorADV probe

6 Bedform formation and evolution

7 Bed configuration with the presence of 2D and 3D ripples. Hydraulic conditions: T w = 3.4 s, H w = 10.7 cm, L w = 7.7 m. Horizontal and transverse resolutions are 1 cm, and 4 cms, respectively. Amalgamated bedforms Survey with the Seatek sensorsSeatek

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

9 Measured dimensionless sandwave height as a function of the Reynolds wave number. Measured dimensionless sandwave length as a function of the Reynolds wave number. Results: sandwaves

10 Dimensionless sandwave length as a function of the Reynolds wave number Measured sandwave vertical growth rate as a function of the Reynolds wave number. harmonics

11 Evolution over time of a measured bed profile

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

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

14 Main findings: Sandwave formation and evolution Sandwave geometry parameters such as height, length, and steepness show less scatter, although considerable, when plotted against R ew than for the case of ψ wc 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 (L sw ) and wavelength of the surface wave (L w ) Experiments for: 10 < ψ wc < 88; < R ew < , and 0.09 < θ < 0.54 For flat bed conditions

15 Results: Ripples superimposed to sandwaves Dimensionless mean ripple wave length as a function of the Reynolds wave number defined as R ew = U wc a / ν. With ψ wcψ wc Dimensionless mean ripple wave height as a function of the Reynolds wave number defined as R ew = U wc a / ν. With ψ wc ψ wc Geometry Ripples over crest

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

17 Measured velocity profilesMeasured velocity profiles after 34 hrs. ΔX = 25.4 cm. Smaller asymmetry Larger asymmetry

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

19 Main 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 R ew for WA and CF. 10 < ψ wc < 88 and < R ew < , and 0.09 < θ < 0.54 For flat bed conditions

20 Thank you! Any questions?

21 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)

22 Shortcomings & Recommendations Use of linear small wave theory (Rigorously: Cnoidal, 2 nd order Stoke’s theory) Use of linear small wave theory (Rigorously: Cnoidal, 2 nd order Stoke’s theory)Cnoidal, 2 nd order Stoke’s theoryCnoidal, 2 nd order Stoke’s theory Include in the calculations of θ the effect of form drag due to ripples and sandwaves. Include in the calculations of θ the effect of form drag due to ripples and sandwaves. Non-linearity due to beach reflection, and wavemaker? Non-linearity due to beach reflection, and wavemaker? So far, work with U c < 20 cm/s So far, work with U c < 20 cm/s Due to a changing bed (Ripples and sandwaves), only mean velocity are suitable for description of global processes. Due to a changing bed (Ripples and sandwaves), only mean velocity are suitable 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 Doppler Velocimeter Profiler)-> resolve turbulence, others…. Better to use of PIV (Particle Image Velocimetry) or ADVP techniques (Acoustic Doppler Velocimeter Profiler)-> resolve turbulence, others….

23 Additional work would include: Additional work would include: To perform refined velocity measurements over an artificial fixed sandwave (If ADV is the only instrument available). To perform refined velocity measurements over an artificial fixed sandwave (If ADV is the only instrument available). -Examine Reynolds stresses distribution and momentum fluxes over three and two dimensional ripples superimposed on sandwaves. -Examine Reynolds stresses distribution and momentum fluxes over three and two dimensional ripples superimposed on sandwaves. - Estimation of the distribution of the friction factor f w, and roughness length z o, over the bedforms. - Estimation of the distribution of the friction factor f w, and roughness length z o, over the 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 morphodynamics of the studied bedforms. - Will help future development of numerical and analytical models dealing with the morphodynamics of the studied bedforms. With movable bed: The effects due to ripples and sandwaves must be separated to obtain a better description of the hydrodynamic processes over the whole flow field. ADV not suitable. It is better to use PIV (Particle Image Velocimetry) or ADVP (Acoustic Doppler Velocity Profiler) techniques where spatial and temporal resolution can be significantly improved. With movable bed: The effects due to ripples and sandwaves must be separated to obtain a better description of the hydrodynamic processes over the whole flow field. ADV not suitable. It is better to use PIV (Particle Image Velocimetry) or ADVP (Acoustic Doppler Velocity Profiler) techniques where spatial and temporal resolution can be significantly improved. 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. 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.

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

25 Go back d = fluid orbital diameter a Shear velocity Shields parameter Mobility number Reynolds wave number

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27 Laser image of a sharp boundary between sand waves (top left corner) and smooth seafloor. Influence of development and migration of bedforms on the burial process Type of bedforms Typical length L Typical height H Length/height ratio Ripples 0.04 – 0.6 m – 0.06 m 8 – 15 Mega ripples 0.6 – 30 m 0.06 – 1.5 m > 15 Sandwaves 30 – 1000 m 1.5 – 15 m > 30 Bedform type (sandy bed) (sandy bed) Related flow Wavelength L (m) Amplitude A (m) Time scale TMigration rate C Ripples Instant flow ~ 1 ~ 0.01 hrs ~ 1 m/day Mega- ripples Storm, surges ~ 10 ~ 0.1 Days ~ 100 m/ye ar SandwavesTide ~ 500 ~ 5 Years ~ 10 m/ye ar Long bed waves Unknown ~ 1500 ~ 5 UnknownUnknown Tidal sandb anks Tide ~ 5000 ~ 10 Century ~ 1 m/year Table 1. Ref. Reineck, H.-E, Singh, I.B., and Wunderlich, F., Table 2. Ref. Characteristics of offshore sand bedforms, Morelissen, R., et al. Coastal Engineering (2003),

28 Also….. Other contributors: ONR program: Theoretical and field: Gallagher et al. (1998) Gallagher et al Theoretical and Laboratory: C. C. Mei, MIT (2002) Theoretical (Stability analysis), numerical modeling, and field of sandwaves: Amos, Németh, Komarova, Holsters, Gekerma, others....

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

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

31 Experimental 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 Back

32 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.

33 Contour map of the sandy bottom and velocity vectors over the centerline of the center sandwave. Flow conditions for waves alone: T w = 2.3 s, L w = 4.9 m, H w = 17.4 cm, h = 60 cm. Average values of morphodynamic characteristics, for ripples: length, l r = 12.7 cm, height, h r = 1.5 cm and speed, c r = 8.4 cm/day; for sandwave: length, l sw = 8.4 m, height, h sw = 40 cm and speed, c sw = 95 m/year. Up to date only two experiments include this type of velocity measurements. Velocity measurements back

34 Go back

35 Go back to recommendations Go back to theoretical background

36 Go back Support

37 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

38 Ratio between measured data and predicted values as a function of the Reynolds wave number, R e : (a) Sandwave length, (b) Sandwave migration speed. Theoretical, Németh et al. (2002) (agree with field data) …but not present study! T m = (Time scale) ??