Wave Turbulence with Applications to Atmospheric and Oceanic Waves

Abstract

We give a review of the main ideas and methods of the wave-turbulence theory and their applications to geophysical fluid dynamics. After having introduced the basic hypotheses leading to kinetic equations for ensembles of weakly nonlinear waves we explain the methods of finding stationary solutions, both for isotropic and weakly anisotropic dispersion relations. We then show how the method can be applied to waves in the atmosphere and ocean and review the known results in this area. Turbulence of the short inertia-gravity waves in the rotating shallow water model is considered at tempered latitudes and in the tropical region, and corresponding stationary spectra are found. Turbulence of the Rossby waves in the same model is also reviewed. Finally, the problem of turbulence of weakly nonlinear internal gravity waves in the continuously stratified fluid is addressed.