Anisotropic turbulence and internal waves in stably stratified flows (QNSE theory)

The quasi-normal scale elimination (QNSE) theory is an analytical spectral theory of turbulence based upon successive elimination of small scales of motion and calculating ensuing corrections to the viscosity and diffusivity. The main results of the theory are analytical expressions for eddy viscosity, eddy diffusivity, and kinetic energy and temperature spectra. Partial scale elimination yields a subgrid-scale representation for large-eddy simulations, whereas the elimination of all fluctuating scales is analogous to the Reynolds averaging. The scale-dependent analysis enables one to put processes on different scales at the spotlight and elucidate their contributions to eddy viscosities and eddy diffusivities. In addition, the method traces the modification of the flow with increasing stratification and recovers growing anisotropy and the effect of the internal waves. The QNSE-based Reynolds-averaged models present a viable alternative to conventional Reynolds stress models. A QNSE model of this kind was tested in the numerical weather prediction system HIRLAM instead of the existing reference Reynolds stress model. The performance of the QNSE model was superior in all simulations where stable stratification was noticeable.