On the diffusion of momentum and mass by internal gravity waves

Abstract

The interaction between short internal gravity waves and a larger-scale mean flow in the ocean is analysed in the Wkbj approximation. The wave field determines the radiation-stress term in the momentum equation of the mean flow and a similar term in the buoyancy equation. The mean flow affects the propagation characteristics of the wave field. This cross-coupling is treated as a small perturbation. When relaxation effects within the wave field are considered, the mean flow induces a modulation of the wave field which is a linear functional of the spatial gradients of the mean current velocity. The effect that this modulation itself has on the mean flow can be reduced to the addition of diffusion terms to the equations for the mass and momentum balance of the mean flow. However, there is no vertical diffusion of mass and other passive properties. The diffusion coefficients depend on the frequency spectrum and the relaxation time of the internal-wave field and can be evaluated analytically. The vertical viscosity coefficient is found to be vv [ape ] 4 x 103cm2/s and exceeds values typically used in models of the general circulation by at least two orders of magnitude.