Energy cascade in internal wave attractors

Sylvain Joubaud
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
Internal gravity waves play an important role in various geophysical flows. Oceans or atmospheres are indeed stratified in density and support the propagation of such waves. They significantly contribute in the mixing of the ocean, the redistribution of energy and momentum in the middle atmosphere or the transport of sediments and plankton. The subsequent mechanism for the energy transfer from large scales of the injected energy to small scales where dissipation occurs is therefore a critical issue in the dynamics of the ocean or the atmosphere, and also an important fundamental question. In this talk, we will focus on the fate of internal gravity waves in a trapezoidal geometry of the confined fluid domain. The peculiar dispersion relation of these waves lead to strong variation of the wave beam upon reflection on a slope. In such a configuration, the focusing of internal waves prevails, leading to convergence of internal wave rays toward closed loops, the internal wave attractors. The high concentration of energy in attractors make them prone to instabilities. We will show that this experimental set-up models a cascade of triadic interactions and provide an efficient energy pathway from global scale motions to small scale overturning events, which induces significant mixing.