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A Hamiltonian Formulation for Long Internal Waves

Yuri V. Lvov·Esteban G. Tabak
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Abstract

A novel canonical Hamiltonian formalism is developed for long internal waves in a rotating environment. This includes the effects of background vorticity and shear on the waves. By restricting consideration to flows in hydrostatic balance, superimposed on a horizontally uniform background of vertical shear and vorticity, a particularly simple Hamiltonian structure arises, which can be thought of as describing a nonlinearly coupled infinite collection of shallow water systems. The kinetic equation describing the time evolution of the spectral energy of internal waves is subsequently derived, and a stationary Kolmogorov solution is found in the high frequency limit. This is surprisingly close to the Garrett--Munk spectrum of oceanic internal waves.

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BibTeXRIS

Yuri V. Lvov, Esteban G. Tabak. 2003-02-22. A Hamiltonian Formulation for Long Internal Waves. https://doi.org/10.1016/j.physd.2004.03.010

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