The stability of plane Couette flow with viscosity stratification

Author:

Craik Alex D. D.

Abstract

The stability of plane Couette flow is examined for liquids in which the viscosity varies with depth. Under suitable conditions, the flow may be stable or unstable at small Reynolds numbers for disturbances with wavelengths long compared with the liquid depth.A mechanism which may be stabilizing or destabilizing is found to derive from the role of diffusion in the neighbourhood of a ‘critical layer’, where the liquid velocity equals the phase velocity of a wave-like disturbance. This mechanism, which requires a viscosity gradient, is quite distinct from that found by Yih (1967) for the case of a viscosity discontinuity. An example is considered, for which these two mechanisms may be of comparable importance.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference8 articles.

1. Yih, C-S. 1954 Stability of parallel laminar flow with a free surface.Proc. 2nd U.S. Congr. of Appl. Mech.623.

2. Yih, C-S. 1963 Stability of liquid flow down an inclined plane Phys. Fluids,6,321.

3. Benjamin, T. Brooke 1957 Wave formation in laminar flow down an inclined plane J. Fluid Mech. 2,554.

4. Lees, L. & Lin, C. C. 1946 Investigation of the stability of the laminar boundary layer in a compressible fluid.NACA Tech. Note no. 1115.

5. Lin, C. C. 1955 The Theory of Hydrodynamic Stability .Cambridge University Press.

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