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Normal modes for a stratified viscous fluid layer

Published online by Cambridge University Press:  12 July 2007

K. F. Gurski  and
R. L. Pego
K. F. Gurski
Affiliation:
National Institute for Standards and Technology, Gaithersburg, MD 20899-8910, USA
R. L. Pego
Affiliation:
Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
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Abstract

We consider internal gravity waves in a stratified fluid layer with rigid horizontal boundaries and periodic boundary conditions on the sides at constant temperature with a small constant viscosity, modelled using the incompressible Navier-Stokes equations. Using operator-theoretic methods to study the damping rates of internal waves we prove there are non-oscillatory wave modes with arbitrarily small damping rates. We provide an asymptotic approximation for these non-oscillatory modes. Additionally, we find that the eigenvalues for damped oscillations are in an explicitly describable half-ring.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 3 , June 2002 , pp. 611 - 625
Copyright
Copyright © Royal Society of Edinburgh 2002

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