On Rayleigh instability in decaying plane couette flow.

Authors: Tillmark, N.T., Alfredsson, P.H.
Document Type: Article
Pubstate: Published
Journal: Appl. Sci. Res.
Volume: 53   187-196
Year: 1994


The inflexion point criterion of Rayleigh is one of the most well-known results in hydrodynamic stability theory but cannot easily be demonstrated experimentally in wall bounded flows. For plane Couette flow, where both walls move with equal speed in opposite directions, it is possible to establish a (time-dependent) inflectional velocity profile if both walls are brought momentarily to rest. If the Reynolds number is high enough a growing stationary instability develops. This situation is ideally suited for flow visualization of the instability. In this paper we show flow visualization experiments and stability calculations of the developing transverse roll cell instability in such a flow at low Reynolds numbers. Although the stability calculations are based on a quasi-stationary velocity profile, the measured and most amplified wave length obtained from the calculations are in excellent agreement.