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Attractor Dimension Estimates For Two-Dimensional Shear Flows, Charles R. Doering, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We study the large time behavior of boundary and pressure-gradient driven incompressible fluid flows in elongated two-dimensional channels with emphasis on estimates for their degrees of freedom, i.e., the dimension of the attractor for the solutions of the Navier-Stokes equations. for boundary driven shear flows and flux driven channel flows we present upper bounds for the degrees of freedom of the form ca Re^3/2 where c is a universal constant, a denotes the aspect ratio of the channel (length/width), and Re is the Reynolds number based on the channel width and the imposed "outer" velocity scale. for fixed pressure …