A model for small-scale ocean turbulence based on wave turbulence theory

It has long been proposed that small-scale oceanic dynamics results from nonlinear processes involving internal gravity waves. The scales in question are not resolved in oceanic models but are accounted for by ad-hoc parameterizations. Physically modelling their turbulent dynamics would therefore be a lever for improving parameterizations in climate models.

In this context, a promising avenue is the weakly nonlinear wave turbulence theory. Its implementation in the case of internal waves in density stratified fluids has nevertheless proved complex and remains an open problem. It is the subject of delicate questions concerning the convergence of the so-called “collision integral” which drives the dynamics in wave turbulence problems.

In this talk, we examine the weak turbulence theory in a linearly stratified fluid from a new perspective. We derive a simplified version of the kinetic equation of internal gravity wave turbulence. The keystone is the assumption that the energy transfers are dominated by a class of nonlocal resonant interactions, known as the “induced diffusion” triads, which conserve the ratio between the wave frequency and the vertical wave number. This kinetic equation allows us to derive scaling laws for the spatial and temporal energy spectra which are consistent with typical exponents observed in the oceans. Our analysis also remarkably shows that the internal wave turbulence cascade is associated to an apparent constant flux of wave action.