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

Estep, D. J. and Verduyn Lunel, S. M. and Williams, R. D. (2000) The Formation, Structure, and Stability of a Shear Layer in a Fluid with Temperature-Dependent Viscosity. California Institute of Technology . (Unpublished)

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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.

Item Type:Report or Paper (Technical Report)
Williams, R. D.0000-0002-9145-8580
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:CACR-2000-187
Persistent URL:
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:28157
Deposited By: Imported from CaltechCACR
Deposited On:24 Mar 2004
Last Modified:03 Oct 2019 03:29

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