A structure-based model for transport in stably stratified homogeneous turbulent flows

We present an extension that allows a recently proposed structure-based model for turbulent scalar transport to account for buoyancy effects. The proposed model is based on a generalization of the Interactive Particle Representation Model (IPRM) and is accompanied by a four-equation transport model that provides the turbulence scales needed for the closure of the complete structure-based model (SBM). The structure tensors and their invariants are used to model the additional buoyancy terms that emerge in the four-equation transport equations. Model parameters are set by matching the asymptotic decay exponents in decaying turbulence. The validity of the model is considered for a large number of different types of stably stratified flows at different Richardson numbers (Ri), showing encouraging results. The complete structure-based model achieves fair agreement with LES and DNS predictions for vertical shear in the presence of vertical mean stratification, while the structure tensors are shown to be suitable for use as diagnostic tools for the morphology of highly anisotropic turbulent structures. Additionally, the proposed model is shown to be sensitive to the variation of the inclination angle θ between the direction of the mean velocity gradient and the orientation of the mean scalar gradient. Furthermore, the model correctly predicts that the evolution of the inverse shear parameter is insensitive to the choice of inclination angle, yielding a turbulent Prandtl number close to unity, in accordance with DNS results.