title: Stochastic mixing model with power law decay of variance.
abstract: A stochastic mixing model based on the law of large numbers is presented that describes the decay of the variance of a conserved scalar in decaying turbulence as a power law, sigma2(c) proportional t(-alpha). A general Lagrangian mixing process is modeled by a stochastic difference equation where the mixing frequency and the ambient concentration are random processes. The mixing parameter lambda is introduced as a coefficient in the mixing frequency in order to account for initial length-scale ratio of the velocity and scalar field and other physical dependencies. We derive a nonlinear integral equation for the probability density function (pdf) of a conserved scalar that describes the relaxation of an arbitrary initial distribution to a delta-function. Numerical studies of this equation are conducted, and it is shown that lambda has a distinct influence on the decay rate of the scalar. Results obtained from the model for the evolution of the pdf are in a good agreement with direct numerical simulation (DNS) data.
authors.affiliation: School of Mathematics, The University of Manchester, Manchester M60 1QD, United Kingdom.
authors.forename: Sergei
authors.initials: S
authors.lastname: Fedotov
authors.forename: Matthias
authors.initials: M
authors.lastname: Ihme
authors.forename: Heinz
authors.initials: H
authors.lastname: Pitsch