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.

References in corpus (2)

• Hamiltonian formalism and the Garrett-Munk spectrum of internal waves in the ocean
• Energy spectra of the ocean's internal wave field: theory and observations

Cited by in corpus (11)

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• Energy cascade in the Garrett-Munk spectrum of internal gravity waves
• On the kinetics of internal gravity waves beyond the hydrostatic regime
• Excitation of interfacial waves via near---resonant surface---interfacial wave interactions
• Wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves
• Oceanic Internal Wave Field: Theory of Scale-invariant Spectra
• 2D Internal Gravity Wave Turbulence