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

Estep, D.J. and Verduyn Lunel, S.M. and Williams, R.D. (2001) Analysis of Shear Layers in a Fluid with Temperature-Dependent Viscosity. Journal of Computational Physics, 173 . pp. 17-60. http://resolver.caltech.edu/CaltechCACR:2001.191

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Abstract

The presence of viscosity normally has a stabilizing effect on the flow of a fluid. Howerver, 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 and numerical 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.


Item Type:Article
Group:Center for Advanced Computing Research
Subject Keywords:a posteriori error estimates, adaptive error control, blow-up, conservation laws, finite element methods, fluid flow, invariant rectangles, plane Couette flow, reaction-diffusion equations, residual errors, shear layers, temperature-dependent viscosity, thermal diffusion
Record Number:CaltechCACR:2001.191
Persistent URL:http://resolver.caltech.edu/CaltechCACR:2001.191
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28195
Collection:CaltechCACR
Deposited By: Imported from CaltechCACR
Deposited On:22 Nov 2004
Last Modified:26 Dec 2012 14:32

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