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Lyapunov stability of ideal stratified fluid equilibria in hydrostatic balance

by: D. D. Holm, B. Long
Nonlinearity, Vol. 2, No. 1. (1 February 1989), pp. 23-35, doi:10.1088/0951-7715/2/1/002  Key: citeulike:12055893

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Abstract

The inviscid dynamics of a continuously stratified, rotating, incompressible fluid in three dimensions is treated in the Boussinesq approximation, assuming hydrostatic balance in the direction of gravity. The dynamics and Lyapunov stability properties of such a fluid are studied by formulating the problem as a noncanonical Hamiltonian system in isopycnal coordinates and using Lyapunov's direct method to establish sufficient conditions for stability of a wide class of equilibrium solutions.


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