Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-01T13:23:23.165Z Has data issue: false hasContentIssue false
  • English
  • Français

A laminar roughness boundary condition

Published online by Cambridge University Press:  26 April 2006

E. O. Tuck  and
A. Kouzoubov
E. O. Tuck
Affiliation:
Applied Mathematics Department, The University of Adelaide, Australia 5005
A. Kouzoubov
Affiliation:
Applied Mathematics Department, The University of Adelaide, Australia 5005 Present address: Centre for Advanced Numerical Computation in Engineering and Science, The University of NSW, Australia 2052.
Get access Rights & Permissions [Opens in a new window]

Abstract

A modified slip boundary condition is obtained to represent the effects of small roughness-like perturbations to an otherwise-plane fixed wall which is acting as a boundary to steady laminar flow of a viscous fluid. In its simplest form, for low local Reynolds number and small roughness slope, this boundary condition involves a constant apparent backflow at the mean surface or, equivalently, represents a shift of the apparent plane boundary toward the flow domain. Extensions of the theory are also made to include finite local Reynolds number and finite roughness slope.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 300 , 10 October 1995 , pp. 59 - 70
Copyright
© 1995 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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions Dover.
Benhalilou, M., Anselmet, F. & Fulachier, L. 1994 Conditional Reynolds stress on a V-grooved surface. Phys. Fluids 6, 2101–2117.Google Scholar
Butcher, J. G. 1876 On viscous fluids in motion. Proc. Lond. Math. Soc. (1) 8, 103–135.Google Scholar
Choudhari, M. 1994 Roughness-induced generation of crossflow vortices in three-dimensional boundary layers. Theor. Comput. Fluid Dyn. 6, 1–30.Google Scholar
Dryden, H. L., Murnaghan, F. D. & Bateman, H. 1956 Hydrodynamics Dover.
Hocking, L. M. 1976 A moving fluid interface on a rough surface. J. Fluid Mech. 76, 801–817.Google Scholar
Jansons, K. M. 1988 Determination of the macroscopic (partial) slip boundary condition for a viscous flow over a randomly rough surface with a perfect slip microscopic boundary condition. Phys. Fluids 31, 15–17.Google Scholar
Lachmann, G. V. 1961 Boundary Layer and Flow Control, Vol. 2. Pergamon.
Mazouz, A., Labraga, C. & Tournier, C. 1994 Behaviour of the Reynolds stress on rough walls. Exp. Fluids 17, 39–44.Google Scholar
Miksis, M. J. & Davis, S. D. 1994 Slip over rough and coated surfaces. J. Fluid Mech. 273, 125–139.Google Scholar
Nye, J. F. 1969 A calculation of the sliding of ice over a wavy surface using a Newtonian viscous approximation. Proc. R. Soc. Lond. A 311, 445–467.Google Scholar
Nye, J. F. 1970 Glacier sliding without cavitation in a linear viscous approximation. Proc. R. Soc. Lond. A 315, 381–403.Google Scholar
Reynolds, A. J. 1965 The swimming of minute organisms. J. Fluid Mech. 23, 241–260.Google Scholar
Richardson, S. 1973 On the no-slip boundary condition. J. Fluid Mech. 59, 707–719.Google Scholar
Schlichting, H. 1979 Boundary Layer Theory, 7th edn. McGraw-Hill.
Taylor, G. I. 1951 Swimming of a waving plate. Proc. R. Soc. Lond. A 209, 447–461.Google Scholar
Tuck, E. O. 1968 A note on a swimming problem. J. Fluid Mech. 31, 305–308.Google Scholar
Tuck, E. O. & Schwartz, L. W. 1994 The slumping liquid bridge. Preprint report, Applied Mathematics Department, University of Adelaide.
dyke, M. Van 1975 Perturbation Methods in Fluid Mechanics Parabolic.
Wang, C. Y. 1994 The Stokes drag due to the sliding of a smooth plate over a finned plate. Phys. Fluids 6 2248–2252.Google Scholar