Attractor dimension estimates for two-dimensional shear flows

[摘要] 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 hows we present upper bounds for the degrees of freedom of the form c alpha Re-3/2 where c is a universal constant, alpha 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 gradient driven channel flows we obtain an upper bound of the form c'alpha Re-2, where c' is another universal positive constant and the Reynolds number is based on a velocity defined by the infimum, over all possible trajectories, of the time averaged mass flux per unit channel width. We discuss these results in terms of physical arguments based on small length scales in turbulent flows. Copyright (C) 1998 Elsevier Science B.V.

[发布日期] 1998-11-15

[效力级别]  Proceedings Paper

[关键词] Navier-Stokes equations;channel flows;global attractor;Hausdorff and fractal dimensions;small length scales;background flows;energy dissipation rate;Reynolds number;Lieb-Thirring inequality