Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-02-11T12:26:56.409Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillating flows over periodic ripples

Published online by Cambridge University Press:  26 April 2006

Tetsu Hara  and
Chiang C. Mei
Tetsu Hara
Affiliation:
Ralph M. Parsons Laboratory, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Chiang C. Mei
Affiliation:
Ralph M. Parsons Laboratory, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Oscillating flows over periodic ripples are of practical as well as scientific interest because of their relevance to beach processes. When either the ripples are sufficiently steep or the amplitude of ambient oscillations large, streamlines of a viscous flow are no longer parallel to the ripple surface. Circulation cells are formed which can help redistribute suspended sediments. Here we study theoretically these cells for a low-viscosity fluid such as pure water over rigid ripples. In particular we have calculated cells whose dimensions are as large as the ripple wavelength and therefore represent viscous effects far above the usual Stokes boundary layer. An idea of Stuart which was originated for stationary mean circulations around a cylinder is extended here. For large ambient amplitude, large oscillating vortices drifting with the ambient flow are found by seeking the stationary cells in a moving coordinate system.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 211 , February 1990 , pp. 183 - 209
Copyright
© 1990 Cambridge University Press

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

Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205.Google Scholar
Caponi, E. A., Fornberg, B., Knight, D. D., Mclean, J. W., Saffman, P. G. & Yuen, H. C. 1982 Calculation of laminar viscous flow over a moving wavy surface. J. Fluid Mech. 124, 347–362.Google Scholar
Davidson, B. J. & Riley, N. 1972 Jets induced by oscillatory motion. J. Fluid Mech. 53, 287–303.Google Scholar
Dore, B. D. 1976 Double boundary layers in standing surface waves. Pure Appl. Geophys. 114, 629–637.Google Scholar
Haddon, E. W. & Riley, N. 1983 A note on the mean circulation in standing waves. Wave Motion 5, 43–48.Google Scholar
Hall, P. 1984 On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347–367.Google Scholar
Kaneko, A. & Honji, H. 1979 Double structures of steady streaming in the oscillatory viscous flow over a wavy wall. J. Fluid Mech. 93, 727–736.Google Scholar
Liu, A.-K. & Davis, S. H. 1977 Viscous attenuation of mean drift in water waves. J. Fluid Mech. 81, 63–84.Google Scholar
Longuet-Higgins, M. S. 1981 Oscillating flow over steep sand ripples. J. Fluid Mech. 107, 1–35.Google Scholar
Lyne, W. H. 1971 Unsteady viscous flow over a wavy wall. J. Fluid Mech. 50, 33–48.Google Scholar
Matsunaga, N., Kaneko, A. & Honji, H. 1981 A numerical study of steady streamings in oscillatory flow over a wavy wall. J. Hydraul. Res. 19, 29–42.Google Scholar
Mei, C. C., Liu, P. L-F. & Carter, T. G. 1972 Mass transport in water waves. Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Rep. 146, 287 pp.Google Scholar
Ralph, M. E. 1986 Oscillatory flows in wavy-walled tubes. J. Fluid Mech. 168, 515–540.Google Scholar
Riley, N. 1965 Oscillating viscous flows. Mathematika 12, 161–175.Google Scholar
Riley, N. 1967 Oscillating viscous flows: review and extension. J. Inst. Maths Applics 3, 419–434.Google Scholar
Riley, N. 1984 Progressive surface waves on a liquid of non-uniform depth. Wave Motion 6, 15–22.Google Scholar
Sato, S., Mimura, N. & Watanabe A. 1984 Oscillatory boundary layer flow over rippled beds In Proc. 19th Conf. on Coastal Engng. pp. 2293–2309.
Schlichting, H. 1955 Boundary-Layer Theory. McGraw-Hill.
Shum, K. T. 1988 A numerical study of vortex dynamics over rigid ripples. Ph.D. Thesis, M.I.T.
Sleath, J. F. A. 1974a Mass transport over a rough bed. J. Mar. Res. 32, 13–24.Google Scholar
Sleath, J. F. A. 1974b Stability of laminar flow at seabed. J. Waterways Harbors and Coastal Engng Div. Proc. ASCE 100 (WW2), 105–122.Google Scholar
Sleath, J. F. A. 1975 A contribution to the study of vortex ripples. J. Hydraul. Res. 13, 315–328.Google Scholar
Sobey, I. J. 1980 On flow through furrowed channels. Part 1. Calculated flow patterns. J. Fluid Mech. 96, 1–26.Google Scholar
Sobey, I. J. 1982 Oscillatory flows at intermediate Strouhal number in asymmetric channels. J. Fluid Mech. 125, 359–373.Google Scholar
Sobey, I. J. 1983 The occurrence of separation in oscillatory flow. J. Fluid Mech. 134, 247–257.Google Scholar
Stuart, J. T. 1963 Unsteady boundary layers In Laminar Boundary Layers, pp. 349–408. Oxford University Press.
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673–687.Google Scholar
Vittori, G. 1989 Non-linear viscous oscillatory flow over a small amplitude wavy wall. J. Hydraul. Res. 27, 267–280.Google Scholar
Wang, C. Y. 1968 On high-frequency oscillatory viscous flows. J. Fluid Mech. 32, 55–68.Google Scholar