Tel-Aviv University
School of Mathematical Sciences
Department of Applied Mathematics

Applied Mathematics Seminar


Tuesday, March 15th, 2011

Schreiber 309, 15:10



Alexander Libin

Ultimate Video Technologies, Tel Aviv



Large Scale Structures as Gradient Lines:

The Case of the Trkal Flow

Abstract:

A specific asymptotic expansion at large Reynolds numbers, R, for the long wavelength perturbations of non-stationary anisotropic helical solutions of the forceless Navier-Stokes equations (Trkal solutions) is efficiently constructed of the Beltrami type terms through multi scaling analysis. The asymptotic procedure is proved to be valid for one specific value of the scaling parameter, namely R^1/2. As a result, large scale structures arise as gradient lines of the energy density determined by the initial conditions for two anisotropic Beltrami flows of the same helicity. The same initial conditions determine the boundaries of the vortex-velocity tubes, containing both streamlines and vortex lines.