Semigeostrophic theory as a Dirac-bracket projection

DOI10.1017/S0022112088002733zbMath0669.76043OpenAlexW2170484858MaRDI QIDQ3823279

Rick Salmon

Publication date: 1988

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0022112088002733

zbMATH Keywords

metric projectionquasi-geostrophic equationsphase-spacesemigeostrophic equationsapproximate dynamical equationsDirac-bracket projectionexact Hamiltonian fluid dynamicsphase-space manifold

Mathematics Subject Classification ID

Related Items (16)

Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves ⋮ A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids ⋮ Mass transport under partially reflected waves in a rectangular channel ⋮ On the Hamiltonian formulation of incompressible ideal fluids and magnetohydrodynamics via Dirac's theory of constraints ⋮ A Hamiltonian structure with contact geometry for the semi-geostrophic equations ⋮ Hamiltonian discontinuous Galerkin FEM for linear, stratified (in)compressible Euler equations: internal gravity waves ⋮ Global well-posedness for the generalized large-scale semigeostrophic equations ⋮ Large-scale semigeostrophic equations for use in ocean circulation models ⋮ The quasi-geostrophic theory of the thermal shallow water equations ⋮ Variational water-wave model with accurate dispersion and vertical vorticity ⋮ Hamiltonian description of the ideal fluid ⋮ A study of surface semi-geostrophic turbulence: freely decaying dynamics ⋮ Extended-geostrophic Hamiltonian models for rotating shallow water motion ⋮ Dirac-bracket approach to nearly geostrophic Hamiltonian balanced models ⋮ Numerical integration of constrained Hamiltonian systems using Dirac brackets ⋮ Generalized LSG models with spatially varying Coriolis parameter

Cites Work

• Practical use of Hamilton's principle
• New equations for nearly geostrophic flow
• Generalized Hamiltonian Dynamics

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