Journal of Fluid Mechanics

Instability due to viscosity stratification

Chia-Shun  Yih a1
a1 Department of Engineering Mechanics, University of Michigan, Ann Arbor

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The principal aim of this paper is to show that the variation of viscosity in a fluid can cause instability. Plane Couette-Poiseuille flow of two superposed layers of fluids of different viscosities between two horizontal plates is considered, and it is found that both plane Poiseuille flow and plane Couette flow can be unstable, however small the Reynolds number is. The unstable modes are in the neighbourhood of a hidden neutral mode for the case of a single fluid, which is entirely ignored in the usual theory of hydrodynamic stability, and are brought out by the viscosity stratification.

(Published Online March 28 2006)
(Received December 14 1965)
(Revised April 20 1966)