On the probability properties of the density gradient of a randomly moving incompressible medium

We study the statistical properties of the density-field gradient of a passive admixture in a randomly moving medium. A expression for the relative gradient-variation field is derived. It is shown that the moments and practically all realizations of the relative gradient-variation field increase exponentially with time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 5, pp. 597–606, May, 1996.This work was partially supported by Russian Foundation for Fundamental Research grant No. 95-05-14247.