Analysis of shear layers in a fluid with temperature-dependent viscosity

The presence of viscosity normally has a stabilizing effect on the flow of a fluid. However, experiments show that the flow of a fluid in which viscos ity decreases as temperature increases tends to form shear layers, narrow r egions in which the velocity of the fluid changes sharply. In general, adia batic shear layers are observed not only in fluids but also in thermo-plast ic materials subject to shear at a high-strain rate and in combustion and t here is widespread interest in modeling their formation. In this paper, we investigate a well-known model representing a 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 subs tantiate the claim that the formation of shear layers can only occur in sol utions of the model when the viscosity decreases sufficiently quickly as te mperature increases and we further analyze the structure and stability prop erties of the layers. (C) 2001 Academic Press.