APPROXIMATE INERTIAL MANIFOLDS AND EFFECTIVE VISCOSITY IN TURBULENT FLOWS

The recently formulated concept of approximate inertial manifolds is exploited as a means for eliminating systematically the fine structure of the velocity field in two-dimensional flows. The resulting iterative procedure does not invoke any statistical properties of the solutions of Navier-Stokes equations. It leads to a modification of those equations, such that effective viscosity-like terms arise in a natural way. The rigorous mathematical considerations can be related to the corresponding physical concepts and intuition. The result leading to a numerical algorithm, essentially a nonlinear Galerkin method, provides a basis for large eddy simulation in which the subgrid model is derived from the properties of the Navier-Stokes equations, rather than from more or less justifiable ad hoc arguments. Some limited speculations concerning the expected results in three dimensions are also offered.