Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-07-03T05:44:27.383Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillatory Flows over a Permeable Wavy Boundary

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, NM 87131, U.S.A.
Philip L.-F. Liu*
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, U.S.A.
*
*Postdoctoral Fellow
**Professor
Get access

Abstract

In this paper viscous boundary layer flows above and inside a permeable wavy bed are studied. The flow motions are driven by an oscillatory horizontal velocity just outside the Stokes boundary layer above the bed. Analytical and numerical solutions are obtained for both the oscillatory velocity component and the steady streaming inside the permeable bed, the Stokes boundary layer and the outer boundary layer. Two specific situations are examined: (1)Weak oscillatory motions over a wavy bed with finite slope and (2) strong oscillatory motions over a small wavy slope. In both situations, the slip (tangential) velocity and the normal velocity do not vanish on the wavy surface because of the permeability. The magnitude of the bed shear stress decreases as the permeability increases. The permeability can also affect significantly the steady streaming patterns; they could change from having two pairs of recirculating cells above an impervious wavy bed to one pair of recirculating cells above a wavy permeable bed.

Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 2 , June 2003 , pp. 279 - 297
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

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

REFERENCES

1Riley, N., “Oscillating Viscous Flows,” Mathematika, 12, pp. 161–175 (1965).Google Scholar
2Stuart, J. T., “Double Boundary Layers in Oscillatory Viscous Flow,” J. Fluid Mech., 24, pp. 673–687 (1966).Google Scholar
3Lyne, W. H., “Unsteady Viscous Flow over a Wavy Wall,” J. Fluid Mech., 50, pp. 33–48 (1971).Google Scholar
4Matsunaga, N., Kaneko, A. and Honji, H., “A Numerical Study of Steady Streamings in Oscillatory Flow over a Wavy Wall,” J. Hydraulic Research, 19(1), pp. 29–42 (1981).Google Scholar
5Vittori, G. and Blondeaux, P., “Mass Transport under Sea Waves Propagating over a Rippled Bed,” J. Fluid Mech., 314, pp. 247–265 (1996).Google Scholar
6Hara, T. and Mei, C. C., “Oscillating Flows over Periodic Ripples,” J. Fluid Mech., 211, pp. 183–209 (1990).Google Scholar
7Blondeaux, P. and Vittori, G., “Vorticity Dynamics in an Oscillatory Flow over a Ripple Bed,” J. Fluid Mech., 226, pp. 257–289 (1991).Google Scholar
8Vittori, G., “Nonlinear Viscous Oscillatory Flow over a Small Amplitude Wavy Wall,” J. Hydraulic Res., 27(2), pp. 267–280 (1989).Google Scholar
9Blondeaux, P. and Vittori, G., Boundary Layer and Sediment Dynamics under Sea Waves, Vol. 4, Advances in Coastal and Ocean Engineering (ed. Liu, P. L.-F.), pp. 133–190 (1999).Google Scholar
10Martin, C. S., “Effect of a Porous Sand Bed on Incipient Sediment Motion,” Water Resources Res., 6(4), pp. 1162–1174 (1970).Google Scholar
11Oldenziel, D. M. and Brink, W. E., “Influence of Suction and Blowing on Entranment of Sand Particles,” J. Hydraulics Div., ASCE, 100(Hy7), pp. 935–949 (1974).Google Scholar
12Conley, D. C. and Inman, D. L., “Ventilated Oscillatory Boundary Layers,” J. Fluid Mech., 273, pp. 261–284 (1994).Google Scholar
13Liu, P. L-F., Davis, M. H. and Downing, S., “Wave-Induced Boundary Layer Flows above and in a Permeable Bed,” J. Fluid Mech., 325, pp. 195–218 (1996).CrossRefGoogle Scholar
14Caponi, E. A., Fornberg, B., Knight, D. D., Mclean, J. W., Saffman, P. G. and Yuen, H. C., “Calculation of Laminar Viscous Flow over a Moving Wavy Surface,” J. Fluid Mech., 124, pp. 247–382 (1982).CrossRefGoogle Scholar