Stochastic theory of compressible turbulent fluid transport

Abstract

We develop a stochastic model for the turbulent transport of passive scalars based on the Fokker–Planck equation for the probability density distribution of the displacements of infinitesimal fluid parcels (“particles”) in random turbulent motion. Such a theory is the microscopic basis behind semiempirical models of turbulent diffusion which apparently have been developed only for incompressible flow. Here, we specifically develop the theory so that it applies to compressible flow. We then apply it to the particular case of stratified mesoscale turbulent transport of tracers in the ocean, and we find that it generalizes the recent parametrization of Gent and McWilliams [J. Phys. Oceanogr. 20, 150 (1990)].