A priori evaluations and least-squares optimizations of turbulence models for fully developed rotating turbulent channel flow

The present study involves a priori tests of pressure-strain and dissipation rate tensor models using data from direct numerical simulations (DNS) of fully developed turbulent channel flow with and without spanwise system rotation. Three different pressure-strain rate models are tested ranging from a simple quasi-linear model to a realizable fourth order model. The evaluations demonstrate the difficulties of developing RANS-models that accurately describe the flow for a wide range of rotation numbers. Furthermore, least-squares based tensor representations of the exact pressure-strain and dissipation rate tensors are derived pointwise in space. The relation obtained for the rapid pressure-strain rate is exact for general 2D mean flows. Hence, the corresponding distribution of the optimized coefficients show the ideal behaviour. The corresponding representations for the slow pressure-strain and dissipation rate tensors are incomplete but still optimal in a least-squares sense. On basis of the least-squares analysis it is argued that the part of the representation that is tensorially linear in the Reynolds stress anisotropy is the most important for these parts.