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Nonlinear Stability of Baroclinic Fronts in a Channel with Variable Topography
Author(s) -
Karsten Richard H.,
Swaters Gordon E.
Publication year - 1996
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1996962183
Subject(s) - baroclinity , nonlinear system , hamiltonian (control theory) , infinitesimal , potential vorticity , variational principle , vorticity , amplitude , classical mechanics , hamiltonian system , hamiltonian formalism , mathematical analysis , mathematics , mechanics , physics , geometry , vortex , quantum mechanics , mathematical optimization , covariant transformation
The governing equations describing baroclinic bottom‐trapped fronts in a channel with variable bottom topography are shown to be a noncanonical Hamiltonian system. The Hamiltonian formalism is exploited to derive a variational principle for arbitrary steady solutions based on an appropriately constrained energy functional. The variational principle is exploited to obtain formal and nonlinear stability conditions. In the infinitesimal amplitude limit, these stability conditions reduce to previously obtained normal mode results for the transverse gradient of the mean frontal potential vorticity.