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Applied Mathematics Colloquium

Friday, February 15, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Stability of Viscoelastic Shear Flow in the Limit of High Reynolds and Weissenberg Numbers

Michael Renardy

Department of Mathematics

Virginia Polytechnic Institute

Blacksburg, VA

Abstract

We consider a limit of the upper convected Maxwell model where both the Weissenberg and Reynolds number are large. This leads to a set of limiting nondissipative equations which include inertia as well as elasticity. These equations admit parallel shear flows with an arbitrary profile of velocity and normal stress. We consider the stability of such flows which are bounded by either walls or free surfaces. In particular, we show that the flow is stabililized if elastic effects are sufficiently strong.