A deterministic model for the propagation of turbulent oscillations

The deterministic point of view on turbulent fluid motion is to consider the Cauchy problem for equations of Navier–Stokes type associated with large Reynolds numbers and with singular initial data. Although the corresponding mathematical study has a lot progressed, it remains limited by fundamental difficulties related to the presence of instabilities. Precisely, the purpose of this article is to show on a realistic two-dimensional model that, up to some extent, such instabilities can be managed. This is achieved in the framework of a supercritical nonlinear geometric optics. The aim is to provide a theory allowing to take into account the interaction of a large amplitude monophase oscillating wave with waves oscillating at smaller frequencies in the other direction. The effect is that very complicated phenomena can occur in the inertial range, including for instance the production of new scales.