Analysis of Shear Layers in a Fluid with Temperature-Dependent Viscosity

• Published in: Journal of computational physics Vol. 173; no. 1; pp. 17 - 60
• Main Authors: Estep, Donald J., Verduyn Lunel, Sjoerd M., Williams, Roy D.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 10.10.2001
• Subjects: blow-up, conservation laws; adaptive error control; plane Couette flow; reaction–diffusion equations; shear layers; temperature-dependent viscosity; finite element methods; fluid flow; invariant rectangles; thermal diffusion; residual errors; a posteriori error estimates
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1006/jcph.2001.6837

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 viscosity decreases as temperature increases tends to form shear layers, narrow regions 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 and there 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 andnumerical tools. We present results to substantiate the claim that the formation of shear layers can only occur in solutions of the model when the viscosity decreases sufficiently quickly as temperature increases and we further analyze the structure and stability properties of the layers.