Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T11:57:20.733Z Has data issue: false hasContentIssue false
  • English
  • Français

Viscous flow through unsteady symmetric channels

Published online by Cambridge University Press:  19 April 2006

P. W. Duck
P. W. Duck
Affiliation:
Department of Mathematics Imperial College, London, S.W. 7 Present address: Department of Mathematics, University of Manchester, England.
Get access Rights & Permissions [Opens in a new window]

Abstract

The high-Reynolds-number (K) flow through a symmetric channel, with walls whose shape is time dependent, is studied. The distortion of the walls is of non-dimensional height $O(K^{-\frac{1}{3}}$) and length O(1), this particular size of perturbation being chosen such that (for the first regime of unsteadiness studied) the effects of the unsteadiness, viscous diffusion and advection all interact nonlinearly in the region of the fluid near the walls.

For this first regime of unsteadiness the problem is solved numerically. This leads on to analytic descriptions for progressively faster time variations of wall shape, and in fact the entire range of unsteadiness is covered for this particular size of distortion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 4 , 27 December 1979 , pp. 635 - 653
Copyright
© 1979 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

Smith, F. T. 1974 J. Inst. Math. Appl. 13, 127.
Smith, F. T. 1976a Q. J. Mech. Appl. Math. 29, 343.
Smith, F. T. 1976b Q. J. Mech. Appl. Math. 29, 365.
Smith, F. T. 1977 J. Fluid Mech. 79, 631.
Smith, F. T. 1978 J. Inst. Math. Appl. 21, 145.
Stewartson, K. & Williams, P. G. 1969 Proc. Roy. Soc. A 312, 181.
Tillet, J. P. K. 1968 J. Fluid Mech. 32, 273.