# Common Hamiltonian structure of the shallow water equations with horizontal temperature gradients and magnetic fields

@article{Dellar2003CommonHS, title={Common Hamiltonian structure of the shallow water equations with horizontal temperature gradients and magnetic fields}, author={Paul J. Dellar}, journal={Physics of Fluids}, year={2003}, volume={15}, pages={292-297} }

The Hamiltonian structure of the inhomogeneous layer models for geophysical fluid dynamics devised by Ripa [Geophys. Astrophys. Fluid Dyn. 70, 85 (1993)] involves the same Poisson bracket as a Hamiltonian formulation of shallow water magnetohydrodynamics in velocity, height, and magnetic flux function variables. This Poisson bracket becomes the Lie–Poisson bracket for a semidirect product Lie algebra under a change of variables, giving a simple and direct proof of the Jacobi identity in place… Expand

#### 36 Citations

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The thermal shallow water equations provide a depth-averaged description of motions in a fluid layer that permits horizontal variations in material properties. They typically arise through an… Expand

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