Probability Distributions of Passive Tracers in Randomly Moving Media
Statistical properties of fluctuations of the density of passive tracer and related random fields in a randomly moving medium are discussed. Diffusion approximation and a Gaussian velocity field model is used. We find probability distributions of density fields and of Jacobians in a chaotically compressible medium. Formulas connecting statistical characteristics of random fields in Lagrangian and in Eulerian coordinates are provided. For an incompressible medium, we analyze statistical properties of the passive scalar field’s gradient, and also statistics of the total gradient and the length of a contour carried in the chaotic flow of an incompressible fluid.
KeywordsRandom Field Stochastic Differential Equation Diffusion Approximation Density Field Passive Tracer
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