Gaussian fields and random flow

Abstract

The high-frequency component of the random solution of a model problem is shown to be statistically orthogonal to the Gaussian component. This is shown to be a consequence of the existence of an equilibrium range. It is concluded that random flow fields can be viewed as being approximately Gaussian only in a very special sense and, in particular, that Wiener–Hermite expansions can provide a useful description only of large-scale hydrodynamical phenomena.