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Slow Damping of Internal Waves in a Stably Stratified Fluid



Katharine F. Gurski, R Kollar, R L. Pego


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.
Royal Society of London


characteristic values, hydrodynamic stability, Pontrjagin space, variable-density Navier Stokes equations, viscous fluid


Gurski, K. , Kollar, R. and Pego, R. (2003), Slow Damping of Internal Waves in a Stably Stratified Fluid, Royal Society of London (Accessed March 4, 2024)
Created February 4, 2003, Updated June 2, 2021