TURBULENT-DIFFUSION OF A PASSIVE IMPURITY

A solution of the diffusion equation in the case of a medium which is diffusing in an inhomogeneous and non-stationary manner is constructed using the Feynman operator formalism. The functional transformation proposed by Stratonovich is used for the "disentanglement of the operator exponent". As a result, the solution is represented in the form of a continual integral which differs from that obtained by Wiener in that, instead of an integral along trajectories, an integral of the velocities of the motion along the trajectories occurs in it. A statistical solution of the diffusion equation is obtained after averaging over random velocities. In the case of Gaussian statistics for the velocity fields or in the case of a spatially homogeneous non-stationary velocity field, continual integration can be carried out in an explicit form in the Markov approximation. In the first case, the result reduces to a renormalization of the coefficient of viscosity (the replacement of the coefficient of molecular viscosity by an effective coefficient of viscosity) and, in the second case, to the replacement of real time by an effective time. A number of papers, a list of which can be found /1/, are concerned with the problem of finding a technique for the "summation" of the coefficients of molecular and turbulent transport (to be specific, we shall speak about diffusion).