An Integral Closure Model for the Vertical Turbulent Flux of a Scalar in a Mixed Layer

Abstract

An integral closure model is proposed for the vertical turbulent transport of a scalar in a mixed layer. The flux divergences at a given level is related to a vertical integral of a weighting function multiplied by the difference between the ensemble mean density of the scalar and the density at the level in question. The weighting function in the closure model is able to account for the anisotropy and inhomogeneity of mixed layer turbulence and so is able to model up-gradient diffusion of heat observed in the tank experiments of Deardorff et al. and the source-dependent flux-gradient relationship observed in numerical experiments of Wyngaard and Brost.