Wiener-Hermite Expansion in Model Turbulence at Large Reynolds Numbers

Abstract

A Wiener‐Hermite functional expansion is used to treat a random initial value process involving the Burgers model equation. The nonlinear model equation has many of the characteristics of the Navier‐Stokes equation. It is found that the functional expansion converges better the larger the separation variable in the correlation function (the nearer to joint normal is the distribution). To the present order, the treatment is similar to a quasinormal assumption. The computations show that the correlation function quickly approaches an equilibrium form for quite different initial values. The power spectrum function approaches an equilibrium form also, where it falls off like the inverse second power of the wavenumber.