An invariant finite-dimensional approximation to the navier-stokes equations and self-excited oscillatory modes of poiseuille flow

Abstract

Abstract A method of determining the finite-dimensional projection of the Navier-Stokes equations onto invariant attractive manifolds is developed. In particular, the projection on a two-dimensional manifold yields an amplitude equation analogous to that discussed by L.D. Landau in /1/. dA dt = A(γ + ∑ ∞ n=1 b 2n A 2n ) with an analytic series in powers of A. The method makes feasible the study of the development of non-linear quasiperiodic perturbations and the occurence of stochastic modes in specific hydrodynamic flows.