Theoretical and Computational Aspects of Turbulence

The computation of turbulent flows necessitate a better understanding of turbulence and the development of algorithms and computational tools which are well adapted to the handling of large numbers of data. Turbulent flows are due to the superposition of a range of small and large eddies which interact and the study of their interaction is an important part of understanding turbulence. An inertial manifold is an exact (quasi-static) interaction law between small and large eddies. In relation with the concept of approximate inertial manifolds (AIM), Foias-Manley-Temam have shown the existence of a simple finite- dimensional manifold lying close to the attractor. By projecting the Navier- Stokes equations on this manifold we obtain a new numerical algorithm called the Nonlinear Galerkin Method. This algorithm is well-adapted to the large time solution of the Navier-Stokes equations and this has been broadly confirmed by the numerical tests which has been performed during this contract. After further tests and studies, this algorithm will soon be available for industrial implementations. (jhd)