New SBL Closure

1. New SBL Closure Boris Galperin Univ. South Florida

2. Stable Boundary Layer ClosureQuasi-Normal Scale Elimination - Dr. Boris Galperin, University of South Florida- momentum temperature and continuity Boussinesq equations Collaborators Semion Sukoriansky, Ben-Gurion University of the Negev,Beer-Sheva, Israel Veniamin Perov, Swedish Meteorological and Hydrological Institute, Sweden Sergej Zilitinkevich, University of Helsinki, Finland • Spectral approach is most appropriate to deal with non-linear, coupled equations. • General idea: Re is small for smallest scales of motion  • Derive perturbative solution for these small scales. • Using this solution perform averaging over infinitesimal band of small scales. Compute corrections to “effective” or “eddy” viscosity and heat diffusivity. Viscosity increases – Re decreases. • Repeat the above procedure for next band of smallest scales. • Do some very patient and creative math with help of Feynman-type diagrams.

3. Stable Boundary Layer ClosureQuasi-Normal Scale Elimination- Dr. Boris Galperin, University of South Florida- REF: Sukoriansky, S., B. Galperin, and I. Staroselsky, 2005: A Quasi-Normal Scale Elimination Model ofTurbulent Flow with Stable Stratification. Phys. Fluids, 17,1 Unique Results Dispersion relation for internal waves in the presence of turbulence Internal wave frequency shift and the criterion of internal wave generation in the presence of turbulence One-dimensional spectra have been calculated analytically confirming the transition from the Kolmogorov, k -5/3 , regime to the stratification-dominated, k -3 ,regime. New expressions for horizontal and vertical eddy viscosities and eddy diffusivities, explicitly accounting for the combined effect of turbulence and internal waves, No critical Richardson number Fr (=nnL2 / N,where nn is eddy viscosity in neutral state, L is the wavenumber of the smallest grid -resolved motion and N is the Brunt-Vaisala frequency

4. Stable Boundary Layer ClosureQuasi-Normal Scale Elimination- Dr. Boris Galperin, University of South Florida- An Application CASES-99 IOP #9 Potential Temperature Wind Speed

5. Stable Boundary Layer ClosureQuasi-Normal Scale Elimination - Dr. Boris Galperin, University of South Florida- CONCLUSIONS • Derivation of the new spectral model of stably stratified turbulence is maximally proximate to first principles; implies quasi-Gaussianity • Model explicitly resolves horizontal-vertical anisotropy • Model accounts for the combined effect of turbulence and waves • Anisotropic turbulent viscosities and diffusivities are in good agreement with experimental data • Anisotropic spectra are calculated. Horizontal energy increases at the expense of vertical energy. Transition to -3 spectra is obtained. • Model yields modification of the classical dispersion relation for internal waves that accounts for turbulence • Model provides subgridscale closures for both LES and RANS • Theory has been implemented in K-ε model of stratified ABL • This K-ε model applies to engineering flows and ABL with/without effects of rotation and stratification using invariant set of constants • Good agreement with BASE, SHEBA and CASES99 data sets has been found for cases of moderate and strong stratification • The model improves predictive skills of HIRLAM in +24h and +48h weather forecast