A non-local second-moment closure model applied to convective boundary layers

Second moment closure is being increasingly invoked to model turbulent mixing. The most common form is a two-equation turbulence model where prognostic equations are solved for the turbulence kinetic energy as well as a quantity involving the length scale, while algebraic relations are written down for second moments. Examples are the Mellor-Yamada type q2-q2l models (Mellor and Yamada 1982, Kantha and Clayson 1994) used in geophysics to model the mixing in the atmospheric boundary layer and the oceanic mixed layer, and k-ε models used in engineering (Rodi 1989). However, a major shortcoming of these models has been the absence of counter-gradient scalar fluxes under convective conditions. One way to remedy this is to appeal to a four-equation model in which prognostic equations are also solved for the temperature and salinity (water vapor in the atmosphere) variances also. When this is done, counter-gradient terms appear in the heat and salt (water vapor) flux equations, in addition to the usual down-the-gradient terms involving the temperature and salinity (water vapor) gradients. We will present results from this non-local model and discuss its performance when compared to LES data on convective mixing.