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L. N. Gutman Conference on Mesoscale Meteorology and Air Pollution, Odessa, Ukraine, September 15 L. N. Gutman Conference on Mesoscale Meteorology and Air Pollution, Odessa, Ukraine, September 15 -17, 2008 Internal Gravity Waves and Turbulence Closure Model for SBL Sergej Zilitinkevich Division of Atmospheric Sciences, Department of Physical Sciences University of Helsinki and Finnish Meteorological Institute Helsinki, Finland Tov Elperin, Nathan Kleeorin and Igor Rogachevskii Department of Mechanical Engineering The Ben-Gurion University of the Negev Beer-Sheba, Israel Victor L’vov Department of Chemical Physics, Weizmann Institute of Science, Israel

Boussinesq Approximation Boussinesq Approximation

Laminar and Turbulent Flows Laminar Boundary Layer Turbulent Boundary Layer Laminar and Turbulent Flows Laminar Boundary Layer Turbulent Boundary Layer

Why Turbulence? Why Not DNS? Number degrees of freedom Why Turbulence? Why Not DNS? Number degrees of freedom

Turbulent Eddies Turbulent Eddies

Laboratory Turbulent Convection After averaging Before averaging Laboratory Turbulent Convection After averaging Before averaging

Velocity Fields Velocity Fields

SBL Equations SBL Equations

Total Energy Total Energy

Total Budget Equations: BL-case Total Budget Equations: BL-case

Total Budget Equations for SBL Total Budget Equations for SBL

Total Budget Equations: BL-case Total Budget Equations: BL-case

Total Energy The turbulent potential energy: The source: Total Energy The turbulent potential energy: The source:

Steady-state of Budget Equations for SBL Steady-state of Budget Equations for SBL

Total Energy Deardorff (1970) Total Energy Deardorff (1970)

Steady-State Form of the Budget Equations Our model Old classical theory Turbulent temperature diffusivity Steady-State Form of the Budget Equations Our model Old classical theory Turbulent temperature diffusivity

vs. vs.

Turbulent Prandtl Number Turbulent Prandtl Number

Total Budget Equations: BL-case in Presents of Gravity Waves Total Budget Equations: BL-case in Presents of Gravity Waves

vs. (Waves) vs. (Waves)

Turbulent Prandtl Number Turbulent Prandtl Number

Anisotropy vs. Anisotropy vs.

vs. vs.

vs. (Waves) vs. (Waves)

Conclusions - Total turbulent energy (potential and kinetic) is conserved - No critical Richardson Conclusions - Total turbulent energy (potential and kinetic) is conserved - No critical Richardson number - Reasonable turbulent Prandtl number from theory - Reasonable explanation of scattering of the observational data by the influence of the largescale internal gravity waves.

References Ø Elperin, T. , Kleeorin, N. , Rogachevskii, I. , and Zilitinkevich, S. References Ø Elperin, T. , Kleeorin, N. , Rogachevskii, I. , and Zilitinkevich, S. 2002 Formation of large-scale semi-organized structures in turbulent convection. Phys. Rev. E, 66, 066305 (1 --15) Ø Elperin, T. , Kleeorin, N. , Rogachevskii, I. , and Zilitinkevich, S. 2006 Tangling turbulence and semi-organized structures in convective boundary layers. Boundary Layer Meteorology, 119, 449 -472. Ø Zilitinkevich, S. , Elperin, T. , Kleeorin, N. , and Rogachevskii, I, 2007 "Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Boundary Layer Meteorology, Part 1: steady-state homogeneous regimes. Boundary Layer Meteorology, 125, 167 -191. Ø Zilitinkevich S. , Elperin T. , Kleeorin N. , Rogachevskii I. , Esau I. , Mauritsen T. and Miles M. , 2008, "Turbulence Energetics in. Stably Stratified Geophysical Flows: Strong and Weak Mixing Regimes". Quarterly Journal of Royal Meteorological Societyv. 134, 793 -799.

Many Thanks to Many Thanks to

THE END THE END

Tturbulence and Anisotropy Isotropy Anisotropy Tturbulence and Anisotropy Isotropy Anisotropy

Total Energy Total Energy

Anisotropy in Observations Isotropy Anisotropy in Observations Isotropy

Equations for Atmospheric Flows Equations for Atmospheric Flows

Budget Equation for TKE Balance in R-space Balance in K-space ( Heisenberg, 1948 ) Budget Equation for TKE Balance in R-space Balance in K-space ( Heisenberg, 1948 ) Isotropy

Mean Profiles Mean Profiles

Turbulent Prandtl Number Turbulent Prandtl Number

Total Budget Equations Ø Turbulent kinetic energy: Ø Potential temperature fluctuations: Ø Flux of Total Budget Equations Ø Turbulent kinetic energy: Ø Potential temperature fluctuations: Ø Flux of potential temperature :

Boundary Layer Height Momentum flux derived Heat flux derived Boundary Layer Height Momentum flux derived Heat flux derived

Calculation Calculation

vs. vs.

Total Budget Equations Ø Turbulent kinetic energy: Ø Potential temperature fluctuations: Ø Flux of Total Budget Equations Ø Turbulent kinetic energy: Ø Potential temperature fluctuations: Ø Flux of potential temperature :

vs. vs.

Temperature Forecasting Curve Temperature Forecasting Curve

Anisotropy vs. Anisotropy vs.