The Weiner-Hermite expansion applied to decaying isotropic turbulence using a renormalized time-dependent base

The problem of decaying isotropic turbulence has been studied using a Wiener-Hermite expansion with a renormalized time dependent base. The expansion is an expansion about Gaussianity. The method followed is to represent the random velocity field as a Wiener-Hermite expansion, substitute the expansion into the Navier-Stokes equations, and deduce differential equations that govern the kernels of the expansion. These equations are integrated to produce the solution to the problem. The theory is completely deductive and uses no ad-hoc modeling approximations. The theory is used to calculate several phenomena of engineering interest: the flatness of turbulence, the Lagrangian autocorrelation function, and the sound radiated by isotropic turbulence. In addition, we propose a model of the energy spectrum and correlation function for large Reynolds number turbulence.