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The inviscid limit of the stochastic Burgers equation is discussed in termsof the level surfaces of the minimising Hamilton-Jacobi function, the classicalmechanical caustic and the Maxwell set and their algebraic pre-images under theclassical mechanical flow map. The problem is analysed in terms of a reduced(one dimensional) action function. We demonstrate that the geometry of thecaustic, level surfaces and Maxwell set can change infinitely rapidly causingturbulent behaviour which is stochastic in nature. The intermittence of thisturbulence is demonstrated in terms of the recurrence of two processes.

A one dimensional analysis of turbulence and its intermittence for the d-dimensional stochastic Burgers equation