Applied Math Seminar: Renormalization and large eddy simulation for a driven Burgers equation in a hydrodynamic regime

Seminar | November 29 | 11 a.m.-12 p.m. | 732 Evans Hall

 Alexandre Chorin, UC Berkeley

 Department of Mathematics

A real-space renormalization group (RNG) is constructed for a randomly-driven Burgers equation, with irrelevant degrees of freedom eliminated sequentially by stochastic parametrization followed by scaling. The connection with more standard implementations of an RNG is spelled out. The parameters in the equation and in the forcing, as well as the construction of the RNG, are chosen so that the resulting random process resembles the one in hydrodynamic turbulence, where the forcing acts on the largest scales and “universality" appears in the intermediate (“inertial") scales. The output of the construction is a discrete model that describes the motion at the coarsest scales in terms of these scales alone, as in large eddy simulation. An example is presented, which exhibits a RNG parameter flow with an inertial range. The broader significance of the results is discusssed.