

Article
An explicit algebraic Reynoldsstress and scalarflux model for stably stratified flows
AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flows. For general twodimensional mean flows, we present a correct way of expressing the Reynoldsstress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynoldsstress tensor and heatflux vector are given. A selfconsistent derivation of this model would, however, require finding a root of a polynomial equation of sixth order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a $K$$\omega$ model and, where needed, nearwall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately selfconsistent. It also fulfil the requirements of realizability.

