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An Isaac Newton Institute Workshop

Pattern Formation in Fluid Mechanics

Global description of patterns far from onset: A case study

Authors: Passot, T (Observatoire de la Cote d'Azur), Ercolani, N (University of Arizona), Indik, R (), Newell, AC (University of Arizona)

Abstract

The Cross-Newell phase diffusion equation and its regularization describe patterns and defects far from onset in large aspect ratio systems with translational and rotational symmetry. We shall show how director field solutions of this equation can be used to describe features of global patterns. The ideas are illustrated in the context of a nontrivial case study of high Prandtl number convection in a large aspect ratio, shallow, elliptical container with heated sidewalls, for which we also have the results of simulation and experiment.