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Published November 2006 | public
Journal Article Open

Stochastic Models for the Kinematics of Moisture Transport and Condensation in Homogeneous Turbulent Flows


The transport of a condensing passive scalar is studied as a prototype model for the kinematics of moisture transport on isentropic surfaces. Condensation occurs whenever the scalar concentration exceeds a specified local saturation value. Since condensation rates are strongly nonlinear functions of moisture content, the mean moisture flux is generally not diffusive. To relate the mean moisture content, mean condensation rate, and mean moisture flux to statistics of the advecting velocity field, a one-dimensional stochastic model is developed in which the Lagrangian velocities of air parcels are independent Ornstein–Uhlenbeck (Gaussian colored noise) processes. The mean moisture evolution equation for the stochastic model is derived in the Brownian and ballistic limits of small and large Lagrangian velocity correlation time. The evolution equation involves expressions for the mean moisture flux and mean condensation rate that are nonlocal but remarkably simple. In a series of simulations of homogeneous two-dimensional turbulence, the dependence of mean moisture flux and mean condensation rate on mean saturation deficit is shown to be reproducible by the one-dimensional stochastic model, provided eddy length and time scales are taken as given. For nonzero Lagrangian velocity correlation times, condensation reduces the mean moisture flux for a given mean moisture gradient compared with the mean flux of a noncondensing scalar.

Additional Information

© 2006 American Meteorological Society Manuscript received 17 November 2005, in final form 3 March 2006 We are grateful for support by the Davidow Discovery Fund, by an Alfred P. Sloan Research Fellowship, and by the National Science Foundation (Grant ATM-0450059). The pseudospectral code used in section 4 is a modified version of the spectral quasigeostropic model developed by Shafer Smith. We gratefully acknowledge helpful suggestions from James Gleeson, Raymond Pierrehumbert, and an anonymous referee.


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