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We summarise a selection of results on the inviscid limit of the stochasticBurgers equation emphasising geometric properties of the caustic, Maxwell setand Hamilton-Jacobi level surfaces and relating these results to a discussionof stochastic turbulence. We show that for small viscosities there exists avortex filament structure near to the Maxwell set. We discuss how thisvorticity is directly related to the adhesion model for the evolution of theearly universe and include new explicit formulas for the distribution of masswithin the shock.

On the stochastic Burgers equation with some applications to turbulence and astrophysics