Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-19T06:43:45.226Z Has data issue: false hasContentIssue false

Small-amplitude oscillatory forcing on two-layer plane channel flow

Published online by Cambridge University Press:  10 March 1997

ADRIAN V. COWARD
Affiliation:
Department of Mathematics and ICAM, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA
YURIKO Y. RENARDY
Affiliation:
Department of Mathematics and ICAM, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA

Abstract

The effect of oscillatory forcing as a dynamic stabilization or destabilization mechanism for two-layer plane Couette–Poiseuille flow at low Reynolds number is studied using numerical and asymptotic methods. The flow is driven by the relative planar motion of the upper boundary and a pressure gradient in the streamwise direction. Both driving forces are composed of a steady part and small-amplitude time-periodic fluctuations. An asymptotic expansion for the growth rates for small amplitudes is developed and the correction terms are quadratic in the amplitudes. The modulations to the steady flow can have either a stabilizing or destabilizing influence depending upon the conditions of flow. Complete stabilization is possible for certain flows which are otherwise unstable owing to the viscosity stratification across the interface. The combined pressure and velocity fluctuations can have an opposite effect on the flow stability to that induced by the separate time-periodic forcing mechanisms.

Type
Research Article
Copyright
© 1997 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.)