A model for the simultaneous transport of heat and water vapor is presented. In an effort to resolve the structure of the entrainment region at the inversion base, models are constructed so as to satisfy realizability as far as possible. Density anomaly and water vapor mixture fraction (specific humidity) are taken as the basic variables. Algebraic expressions for the third moments are derived from first principles, and contain no adjustable constants. Separate equations are carried for the dissipation of each variance, constructed to give rational behavior of all time scale ratios. New forms for relaxation and cross-dissipation terms are constructed in such a way as to guarantee realizability. We describe how realizability was used as a tool to construct these models. We present preliminary results without mean velocity gradients for a dry surface mixed layer leaving the land and starting over water, producing a stable internal humidity boundary layer, but with large fluxes of sensible heat and water vapor (local advection).
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Lumley, J.L., Mansfield, P. Second order modeling of turbulent transport in the surface mixed layer. Boundary-Layer Meteorol 30, 109–142 (1984). https://doi.org/10.1007/BF00121951
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DOI: https://doi.org/10.1007/BF00121951