Special Particle Physics Seminar: Turbulence as Random Geometry

Abstract:

We review a geometric approach to the Turbulence where the vorticity is confined to an ensemble of vortex cells of random sizes and shapes. The velocity circulation as a functional of the loop satisfies certain Loop Equation derived in early 90-ties. We present some analytic and numerical solutions of this equation and compare them with recent large scale numerical simulations. The more general approach is to treat Turbulence as some Gibbs statistics with the effective Hamiltonian to be determined from the Navier-Stokes equations and the symmetry principles. 

We present such an effective Hamiltonian and describe the possible analytical and numerical methods to study it. We find surprising relation of this theory to the 2D string theory and matrix models of Gravity. There are some unanswered questions, requiring further numerical simulations and theoretical investigation.

Seminar Organizers: Prof. Erez Etzion & Dr. Liron Barak