Probability Distribution of a Passive Scalar in Isotropic Turbulence

Abstract

In this letter, we present developments of the Hamiltonian approach to problems of the probability distribution for a passive scalar in isotropic turbulence, and also considers specific applications of the modified Prelle-Singer procedure to turbulence models. The following key questions are discussed and solved: what is the general dynamical structure of the resulting scale equation permitted by passive scalar turbulence models? What are the general requirements of the relations between canonical variables and the canonical variabes representation for turbulence by using canonical variables? It is shown that the existence of the Haniltonian representation in turbulence is a privilege of only turbulence systems for which the variational principle of least action is impossible The master equation of the probability distribution of a passive scalar in isotropic turbulence can also be deduced explicitly.