STOCHASTIC BURGERS EQUATION IN D-DIMENSIONS - A ONE-DIMENSIONAL ANALYSIS: HOT AND COOL CAUSTICS AND INTERMITTENCE OF STOCHASTIC TURBULENCE

We give a one dimensional analysis of the solution v^μ of the stochastic Burgers equation in d dimensions, with viscosity μ²~0, as obtained by Davies, Truman and Zhao. Our analysis shows how the graph of a simple action functional in one space variable can be used to decompose the caustics into hot and cool parts. The inviscid limiting Burgers velocity field has a jump discontinuity across a cool part but is continuous as you cross the hot part. Our analysis also enables us to get a hold on the intermittence of stochastic turbulence in terms of the recurrence of a one dimensional stochastic process ζ simply related to the reduced action. Some detailed examples are discussed.