The WeinerHermite expansion applied to decaying isotropic turbulence using a renormalized timedependent base
Abstract
The problem of decaying isotropic turbulence has been studied using a WienerHermite 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 WienerHermite expansion, substitute the expansion into the NavierStokes 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 adhoc 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 November 1977
 Bibcode:
 1977PhDT.......110H
 Keywords:

 Functional Analysis;
 Isotropic Turbulence;
 Normal Density Functions;
 Time Dependence;
 Functions (Mathematics);
 Normalizing (Statistics);
 Problem Solving;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer