A Hamiltonian Formulation for Long Internal Waves

Details A Hamiltonian Formulation for Long Internal Waves A Hamiltonian Formulation for Long Internal Waves

2002-08-16

arxiv.org/abs/math-ph/0208022v2

Physica D: Vol 195/1-2 pp 106-122, 2004.

Physics

Mathematical Physics

Scientific paper

10.1016/j.physd.2004.03.010

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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