Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T15:57:06.509Z Has data issue: false hasContentIssue false
  • English
  • Français

Instability of a periodic boundary layer in a stratified fluid

Published online by Cambridge University Press:  29 March 2006

R. M. Robinson  and
A. D. McEwan
R. M. Robinson
Affiliation:
CSIRO, Division of Atmospheric Physics, Aspendale, Victoria 3195, Australia
A. D. McEwan
Affiliation:
CSIRO, Division of Atmospheric Physics, Aspendale, Victoria 3195, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

It has been found that the periodic boundary layer formed on a vertically oscil-lating vertical wall bounding a stratified fluid is liable to two distinct modes of wavelike instability. In the first, which arises when the oscillation frequency ω is lower than 0·7 times the buoyancy frequency N, the phase lines are aligned horizontally. The second mode, in which the phase lines are aligned at 45° or more to the horizontal, becomes dominant as ω is increased above 0·9 N.

In distinction from the unstratified periodic Stokes layer, there appears to be, for ω in the vicinity of N, a definite low threshold to the boundary-layer Stokes-Reynolds number (defined as Wo/(2ων)½, where Wo is the maximum vertical wall velocity and v is the kinematic viscosity) above which the instability is sustained a t a detectable level.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 1 , 11 March 1975 , pp. 41 - 48
Copyright
© 1975 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

Collins, J. I. 1963 Inception of turbulence at the bed under periodic gravity waves. J . Ceophys. Res. 68, 6007.Google Scholar
Conrad, P. W. & Criminale, W. O. 1965 The stability of time-dependent laminar flow: parallel flows. 2. Angew. Math. Phys. 16, 233.Google Scholar
Grosch, C. E. & Salwen, H. 1968 Stability of steady and time-dependent plane Poiseuille flow. J . Fluid Mech. 34, 177.Google Scholar
Hart, J. E. 1971 A possible mechanism for boundary layer mixing and layer formation in a stratified fluid. J. Phys. Oceanog. 1, 258.Google Scholar
Kerczek, C. VON 1973 On the stability of Stokes layers. Ph.D. thesis, Dept. Mech. & Materials Sci., The Johns Hopkins University.
Kerczek, C. VON & Dayis, S. H. 1974 Linear stability theory of oscillatory Stokes layers. J. Fluid Mech. 62, 753.Google Scholar
Mowbray, D. E. & Rarity, B. S. H. 1967 A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech. 28, 1.Google Scholar