Gurski, K.
, Kollar, R.
and Pego, R.
(2003),
Slow Damping of Internal Waves in a Stably Stratified Fluid, Royal Society of London (Accessed April 27, 2026)
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Slow Damping of Internal Waves in a Stably Stratified Fluid
Published
Author(s)
, R Kollar, R L. Pego
Abstract
We study the damping of internal gravity waves in a stably stratified fluid with constant viscosity in two- and three-dimensional bounded domains. For the linearized Navier-Stokes equations for incompressible flow with no-slip boundary conditions that model this fluid, we prove there are non-oscillatory normal modes with arbitrarily small exponential decay rates. The proof is very different from that for a horizontally periodic layer and depends on a structure theorem for compact operators which are self-adjoint with respect to an indefinite scalar product in a Hilbert space. We give a complete proof of this theorem, which is closely related to results of Pontrjagin.Citation
Royal Society of London
Pub Type
Journals
Keywords
characteristic values, hydrodynamic stability, Pontrjagin space, variable-density Navier Stokes equations, viscous fluid
Citation
Issues
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Created February 4, 2003, Updated June 2, 2021