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Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations
A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations using the conservation for energy and potential enstrophy is presented. Different mechanisms, such as vortical flows and emission of gravity waves, emerge from different conservation laws for total energy and potential enstrophy. The equations are constructed using exterior differential forms and self-adjoint operators, and result in the sum of two Nambu brackets-one for the vortical flow and one fordoi:10.3390/fluids2020024 fatcat:e3sn55gyejdcxaqjwfwqf23zju