The Formation, Structure, and Stability of a Shear Layer in a Fluid with Temperature-Dependent Viscosity

Abstract

The presence of viscosity normally has a stabilizing effect on the flow of a fluid. However, experiments show that the flow of a fluid might form shear bands or shear layers, narrow bands in which the velocity of the fluid changes sharply. In general, adiabatic shear layers are observed not only in fluids but also in thermo-plastic materials subject to shear at a high-strain rate and in combustion. Therefore there is widespread interest in modeling the formation of shear layers. In this paper we investigate the basic system of conservation laws for a one-dimensional flow with temperature-dependent viscosity using a combination of analytical and numerical tools. We present results to substantiate the claim that the formation of shear layers is due to teh fact that viscosity decreases sufficiently quickly as temperature increases and analyze the structure and stability properties of the layers.

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