Flow Dynamics and Bed Resistance of Wave Propagation over Bed Ripples
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 137, Issue 2
Abstract
The viscous, two-dimensional, free-surface flow induced by the propagation of nonlinear water waves over a rigid rippled bed was simulated numerically. The simulations were based on the numerical solution of the Navier-Stokes equations subject to fully nonlinear free-surface boundary conditions and appropriate bottom, inflow, and outflow boundary conditions. The equations were properly transformed so that the computational domain became time-independent. A hybrid scheme was used for the spatial discretization with finite differences in the streamwise direction and a pseudospectral approximation with Chebyshev polynomials in the vertical direction. A fractional time-step scheme was used for the temporal discretization. Over the rippled bed, the wave boundary layer thickness increased significantly, while vortex shedding at the ripple crest generated alternating circulation regions over the ripple trough. The velocity of the Eulerian drift profile was opposite to the direction of wave propagation far above the ripples, whereas close to the bed, its magnitude was influenced by the ripples up to a height of about six times the ripple height above the ripple crest. The amplitude of the wall shear stress on the ripples increased with increasing ripple steepness, whereas the amplitude of the corresponding friction drag force on a ripple was insensitive to this increase. The amplitude of the form drag force attributable to the dynamic pressure increased with increasing ripple steepness; therefore, the percentage of friction in the total drag force decreased with increasing ripple steepness. The period-averaged drag forces on a ripple were very weak, while the influence of form drag increased with increasing ripple steepness.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The financial support by the Research Committee (B.131) of the University of Patras under the “K. Karatheodori Program” is greatly appreciated.
References
Barr, B. C., Sinn, D. N., Pierro, T., and Winters, K. B. (2004). “Numerical simulation of turbulent, oscillatory flow over sand ripples.” J. Geophys. Res., 109(C09009), 1–19.
Blondeaux, P., Foti, E., and Vittori, G. (2000). “Migrating sea ripples.” Eur. J. Mech. B, Fluids, 19, 285–301.
Blondeaux, P., and Vittori, G. (1991). “Vorticity dynamics in an oscillatory flow over a rippled bed.” J. Fluid Mech., 226, 257–289.
Davies, A. G., and Villaret, C. (1999). “Eulerian drift induced by progressive waves above rippled and very rough beds.” J. Geophys. Res., 104(C1), 1465–1488.
Dimas, A. A., and Dimakopoulos, A. S. (2009). “Surface roller model for the numerical simulation of spilling wave breaking over constant slope beach.” J. Waterway, Port, Coastal, Ocean Eng., 135(5), 235–244.
Fredsøe, J., Anderson, K. H., and Sumer, B. M. (1999). “Wave plus current over a ripple-covered bed.” Coastal Eng., 38(4), 177–221.
Fredsøe, J., and Deigaard, R. (1992). Mechanics of coastal sediment transport, World Scientific, Singapore.
Gotlieb, D., and Orszag, S. A. (1977). Numerical analysis of spectral methods: Theory and applications, Society for Industrial and Applied Mathematics, Philadelphia.
Grilli, S. T., and Horrillo, J. (1997). “Numerical generation and absorption of fully nonlinear periodic waves.” J. Eng. Mech., 123(10), 1060–1069.
Huang, C. J., and Dong, C. M. (2002). “Propagation of water waves over rigid rippled beds.” J. Waterway, Port, Coastal, Ocean Eng., 128(5), 190–201.
Longuet-Higgins, M. S. (1981). “Oscillating flow over steep sand ripples.” J. Fluid Mech., 107, 1–35.
Malarkey, J., and Davies, A. G. (2004). “An eddy viscosity formulation for oscillatory flow over vortex ripples.” J. Geophys. Res., 109(C09016), 1–13.
Marin, F. (2004). “Eddy viscosity and Eulerian drift over rippled beds in waves.” Coastal Eng., 50(3), 139–159.
Nielsen, P. (1981). “Dynamics and geometry of wave-generated ripples.” J. Geophys. Res., 86(C7), 6467–6472.
O’Donoghue, T., Doucette, J. S., van der Werf, J. J., and Ribberink, J. S. (2006). “The dimensions of sand ripples in full-scale oscillatory flows.” Coastal Eng., 53(12), 997–1012.
Ridler, E. L., and Sleath, J. F. A. (2000). “Effect of bed roughness on time-mean drift induced by waves.” J. Waterway, Port, Coastal, Ocean Eng., 126(1), 23–29.
Scandura, P., Blondeaux, P., and Vittori, G. (2000). “Three-dimensional oscillatory flow over steep ripples.” J. Fluid Mech., 412, 355–378.
Schlichting, H. (1979). Boundary layer theory, McGraw-Hill, New York.
Swart, D. H. (1976). “Coastal sediment transport.” Rep. R968: Part 1, Delft Hydraulics, Delft, The Netherlands.
Wiberg, P. L., and Harris, C. E. (1994). “Ripple geometry in wave-dominated environments.” J. Geophys. Res., 99(C1), 775–789.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 137 • Issue 2 • March 2011
Pages: 64 - 74
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Oct 22, 2009
Accepted: Jun 9, 2010
Published online: Jun 12, 2010
Published in print: Mar 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.