The relationship between a Wiener-Hermite expansion and an energy cascade

A theory of Burgers turbulence involving a truncated Wiener-Hermite expansion of the velocity field is described. Numerical analysis shows that the theory predicts an insufficient rate of energy decay for Reynolds numbers larger than two. It is shown that an energy cascade in wave number space corresponds to a cascade of energy up through successive terms of the Wiener-Hermite expansion. Results indicate that Gaussianity has no bearing on the rate of convergence of an expansion whose white noise function is associated with the initial state.