Simple modification of two-equation models for non-neutral flow

It has been recognized that the turbulent length scale or time scale must be calculated as a dynamic variable in any model that aims to simulate atmospheric flows over heterogeneous surfaces adequately. A two-equation closure approach based on transport equations for the turbulent kinetic energy, k, and some supplementary characteristic, φ, does not require a predefined mixing length and seems to be naturally suited for a modelling of such flows. However, the fundamental uncertainty about what is the best way to treat the dissipation mechanisms in the presence of vegetation under conditions of non-neutral air stratification is still the main problem in development of models based on this closure. A number of researchers have emphasized that such models suffer from ambiguities in description of both plant drag and buoyancy effects in k- and φ – equations. Recently Sogachev and Panferov (2006) enhanced the description of dissipation mechanism in such models and extended their generality and applicability to neutral inhomogeneous canopy flow. The suggested modification of two-equation models to account for plant drag was found robust. It is quite universal, i.e. of the same type for all two-equations models considered, and performs well for wide range of canopies. Here we improve further the description of dissipation mechanism in two-equation models with reference to non-neutral flow. The approach is similar to the one implemented for the plant drag. The modification proposed by Sogachev and Panferov (2006) is due to the fact that the model constants estimated experimentally for ‘free-air' flow do not allow for adequate reconstruction of the ratio between the production and dissipation rates of turbulent kinetic energy, ε, in the vegetation canopy and have to be adjusted. In similar way we corrected the production/dissipation ratio in presence of buoyancy force. The numerical experiments carried out for non-neutral flow with k-ω (where ω is specific dissipation of k, ω=ε/k) model showed that the modification performs well and that the potential of two-equation models, which are already fully implemented in engineering, could be realized with the same success in the environmental research. A number of environmental applications are given as examples.