Numerical Study of the Burgers' Model of Turbulence Based on the Characteristic Functional Formalism

Abstract

The one‐dimensional Burgers' model of turbulence is investigated by computing the functional integral expression for the correlation function, based on the Hopf theory of statistical hydromechanics, with the aid of a high‐speed computer. The initial probability distribution of the velocity is assumed to be normal with zero mean and with a Gaussian covariance function. The manner in which the energy decay curve changes under variation of the Reynolds number $R$ implies the existence of a certain asymptotic curve for $\mathrm{R\hspace{0.17em}\to \hspace{0.17em}\infty }$ . The values obtained for the correlation function at some instants indicate that the inverse‐square law for the energy spectrum holds in some wavenumber range for high values of $R$ .