Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-29T07:43:46.705Z Has data issue: false hasContentIssue false
  • English
  • Français

The Porous Effect on the Bottom Instability Under Partially Standing Waves

Published online by Cambridge University Press:  05 May 2011

Shih-Chun Hsiao  and
Philip L.-F. Liu
Shih-Chun Hsiao*
Affiliation:
Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM87131, U.S.A.
Philip L.-F. Liu*
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14850–2488, U.S.A.
*
* Professor
** Postdoctoral Fellow
Get access

Abstract

In this paper, we extended Blondeaux [1], Liu, et al. [2] and Mei and Yu's [3] theories to study the porous effect on instability of rippled bed under the partially standing surface waves. Comparisons are made with both Blondeaux and Mei & Yu's theoretical predictions and experimental data performed by many other authors. We found that based on the linear instability analysis and the parameter regimes we explored the percolation effect can change the threshold conditions by 10 ∼ 20 percent and the seepage force is negligible up to O(∈). Furthermore, the steady streamings with or without porous effect show the considerable difference in intensities at the same locations and it might change the sediment transport rate especially the suspended load.

Type
Articles
Information
Journal of Mechanics , Volume 18 , Issue 2 , June 2002 , pp. 53 - 66
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Blondeaux, P., “Sand Ripples under Sea Waves- Part 1: Ripple Formation,” J. Fluid Mech., 218, pp. 1–17 (1990).CrossRefGoogle Scholar
[2]Liu, P. L-F., Davis, M. H. and Downing, S., “Wave-Induced Boundary Layer Flows above and in a Permeable Bed,” 325, pp. 195–218 (1996).Google Scholar
[3]Mei, C. C. and Yu, Jie, “The Instability of Sand Ripples Under Partially Standing Surfaces Waves,” Phys. Fluids., 9(6), pp. 1606–1620 (1997).CrossRefGoogle Scholar
[4]Longuet-Higgins, M. S., “Mass Transport in Water Waves,” Phil. Trans. R. Soc. Lond. A, 245, pp. 535–581 (1953).Google Scholar
[5]Sleath, J. F. A., “On Rolling-Grain Ripples,” J. Hydraulic. Res., 14, pp. 69–81 (1976).CrossRefGoogle Scholar
[6]Vittori, G., “Nonlinear Viscous Oscillatory Flow over a Small Amplitude Wavy Wall,” J. Hydraulic. Res., 27(2), pp. 267–280 (1989).CrossRefGoogle Scholar
[7]Hara, T. and Mei, C. C., “Oscillating Flows over Periodic Ripples,” J. Fluid Mech., 211, pp. 183–209 (1990).CrossRefGoogle Scholar
[8]Vittori, G. and Blondeaux, P., “Sand Ripples Under Sea Waves? Part 2: Finite-Amplitude Development,” J. Fluid Mech., 248, pp. 19–39 (1990).CrossRefGoogle Scholar
[9]Foti, E. and Blondeaux, P., “Sea Ripple Formation: The Turbulent Boundary Layer Case,” Coastal Engrg., 25, pp. 227–236 (1995).CrossRefGoogle Scholar
[10]Sleath, J. F. A., “Velocities and Shear Stresses in Wave-Current Flows,” J. Geophys. Res., 96, pp. 15237–15244 (1991).CrossRefGoogle Scholar
[11]Hsiao, S. C. and Liu, P. L-F., “Oscillatory Flows over Permeable Ripples,” submitted to Proc. R. Soc. Lond. A (2002).Google Scholar
[12]Grass, J. A. and Ayoub, N. M., “Bed Load Transport of Fine Sand by Laminar and Turbulent Flow,” Proc. 18th Int. Conf. Coastal Engrg. ASCE, pp. 1589–1599 (1982).CrossRefGoogle Scholar
[13]Abou-Seida, M. M., “Bed Load Function due to Wave Action,” University of California, Berkeley, Hydraulic Engineering Laboratory, Report No. HEL-2-11 (1965).Google Scholar
[14]Sleath, J. F. A., “Measurements of Bed Load in Oscillatory Flow,” J. Waterway Port Coastal Ocean Engrg. Div. ASCE, 104, pp. 291–307 (1978).CrossRefGoogle Scholar
[15]Fredsoe, J., “On the Development of Dunes on Erodible Channels,” J. Fluid Mech., 64, pp. 1–16 (1974).CrossRefGoogle Scholar
[16]Blondeaux, P., Sleath, J. F. A. and Vittori, G., “Experimental Data on Sand Ripples in an Oscillatory Flow,” Rep. 01/88, Inst. Hydraulics, University of Genova (1988).Google Scholar
[17]Sleath, J. F. A., Sea Bed Mechanics, Wiley (1984).Google Scholar
[18]Abramowitz, and Stegun, , Handbook of Mathematical Functions, Dover (1965).Google Scholar
[19]Manohar, M., “Mechanics of Bottom Sediment Movement due to Wave Action,” US Army, Beach Erosion Board Tech. Memo 75 (1955).Google Scholar
[20]Kennedy, J. F. and Falcon, M., “Wave-Generated Sediment Ripples,” MIT Hydrodynamics Lab Report (1965).Google Scholar
[21]Horikawa, K. and Watanabe, A., “A Study on Sand Movement due to Wave Action,” Coastal Engrg. Japan, 10, pp. 39–57 (1967).CrossRefGoogle Scholar
[22]Martin, C. S., “Effect of a Porous Bed on Incipient Sediment Motion,” Water Resources Res., 6(4), pp. 1162–1174 (1970).CrossRefGoogle Scholar
[23]Martin, C. S. and Aral, M. M., “Seepage Force on Interfacial Bed Particles,” J. Hydralics Div., ASCE, 97(Hy 7), pp. 1081–1100 (1971).CrossRefGoogle Scholar