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

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 R → ∞. 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.