Lefschetz Center for Dynamical Systems Seminar
Abstract: I will present the derivation and analysis of the anisotropic averaged Euler equations for incompressible hydrodynamics. This model is obtained by "fuzzying" the Lagrangian flow map of the Euler equations over spatial scales smaller than some number alpha, and averaging on the volume-preserving diffeomorphism group. The resulting system of equations evolves the pair $(u,F)$, where $ u $ the macroscopic velocity field and $ F $ is a symmetric fluctuation tensor measuring the deviation of the flow from the mean. After solving this system, one may then "correct" the macroscopic velocity to order $ alpha^{2} $. Well-posedness results will be given, and the channel flow approximation will be discussed.
<--- 2000 Index