Internal gravity waves: From instabilities to turbulence

We review the mechanisms of steepening and breaking for internal gravity waves in a continuous density stratification. After discussing the instability of a plane wave of arbitrary amplitude in an infinite medium at rest, we consider the steepening effects of wave reflection on a sloping boundary and propagation in a shear flow. The final process of breaking into small-scale turbulence is then presented. The influence of those processes upon the fluid medium by mean flow changes is discussed. The specific properties of wave turbulence, induced by wave-wave interactions and breaking, are illustrated by comparative studies of oceanic and atmospheric observations, as well as laboratory and numerical experiments. We then review the different attempts at a statistical description of internal gravity wave fields, whether weakly or strongly interacting.