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A Hamiltonian Formulation for Long Internal Waves
Physica D 195, 106 (2004).

Yuri Lvov1

Department of Mathematical Sciences

Rensselaer Polytechnic Institute

Esteban G. Tabak2

Courant Institute of Mathematical Sciences

New York University


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. In the high frequency limit, the Coriolis effects may be neglected, and a family of stationary Kolmogorov solutions can be found, which includes the Garrett-Munk spectrum of oceanic internal waves.

submitted to Physica D

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Next: Introduction
Dr Yuri V Lvov 2007-01-17