Nonlinear galerkin method and subgrid-scale model for two-dimensional turbulent flows

The nonlinear Galerkin method, derived by Marion and Temam from results in dynamical systems theory, is investigated in the framework of numerical simulation of two-dimensional incompressible turbulent flows. We use the nonlinear Galerkin method together with a hyperviscosity subgrid-scale parametrization. We state the theoretical background, define the scheme, and derive some technical improvements for the method. We also report numerical experiments conducted for freely decaying as well as forced turbulence. Our main conclusion is that the performance of the nonlinear Galerkin method is important only if the dissipation range is large.This work was supported by Contract D.R.E.T. 90/1551/A000: Développement d'algorithmes de simulation numérique des équations de Navier-Stokes.