A Hamiltonian Formulation for Long Internal Waves
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.
Cite
@article{arxiv.math-ph/0208022,
title = {A Hamiltonian Formulation for Long Internal Waves},
author = {Yuri V. Lvov and Esteban G. Tabak},
journal= {arXiv preprint arXiv:math-ph/0208022},
year = {2009}
}