CONVERGENCE OF GALERKIN SOLUTIONS USING KARHUNEN-LOEVE EXPANSIONS OF INHOMOGENEOUS 1-D TURBULENCE

Abstract

The rate of convergence of the Karhunen-Loeve expansion of an inhomogeneous, instantaneous random field is compared with that of Fourier expansion in relation to the Reynolds number. The model turbulence is generated by solving the Burgers' equation with random forcing. The coefficients of the Fourier expansion are determined by a Galerkin solution scheme. The results show obvious superiority of the Karhunen-Loeve expansion, especially for high Reynolds number flows.