SUBGRID MODELING AND THE INTERACTION OF SMALL AND LARGE WAVELENGTHS IN TURBULENT FLOWS

Modelling the interaction of small and large eddies in a turbulent flow is an important part of the understanding of turbulence and an important task in subgrid modelling and computational fluid dynamics. In this article we describe a new approach to this problem based on dynamical systems theory: the principle is that the turbulent flow is described by a compact attractor that may be a complicated set (fractal) and we approximate the attractor by smooth finite dimensional manifolds: these manifolds provide an approximate interaction law for small and large eddies. After describing the method we report on numerical computations based on this approach. They show an improvement in stability and accuracy and a significant gain in computing time.