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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 L. N. Gutman Conference on Mesoscale Meteorology and Air Pollution, Odessa, Ukraine, September 15-17, 2008
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Boussinesq Approximation
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Laminar and Turbulent Flows Laminar Boundary Layer Turbulent Boundary Layer
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Why Turbulence? Number degrees of freedom Why Not DNS?
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Turbulent Eddies
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Laboratory Turbulent Convection Before averaging After averaging
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Velocity Fields
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SBL Equations
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Total Energy
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Total Budget Equations: BL-case
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Total Budget Equations for SBL
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Total Budget Equations: BL-case
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Total Energy The source: The turbulent potential energy:
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Steady-state of Budget Equations for SBL
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Total Energy Deardorff (1970)
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Steady-State Form of the Budget Equations Turbulent temperature diffusivity Our model Old classical theory
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vs. vs.
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Turbulent Prandtl Number
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Total Budget Equations: BL-case in Presents of Gravity Waves
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vs. (Waves) vs. (Waves)
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Turbulent Prandtl Number
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Anisotropy vs.
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vs. vs.
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vs. (Waves) vs. (Waves)
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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 large- scale internal gravity waves.
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References 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) 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. 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. Zilitinkevich S., Elperin T., Kleeorin N., Rogachevskii I., Esau I., Mauritsen T. and Miles M., 2008, "Turbulence Energetics inStably Stratified Geophysical Flows: Strong and Weak Mixing Regimes". Quarterly Journal of Royal Meteorological Societyv. 134, 793-799.
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Many Thanks to
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THE END
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Tturbulence and Anisotropy IsotropyAnisotropy
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Total Energy
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Anisotropy in Observations Isotropy
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Equations for Atmospheric Flows
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Budget Equation for TKE Balance in R-space Balance in K-space ( Heisenberg, 1948 ) Isotropy
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Mean Profiles
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Turbulent Prandtl Number
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Total Budget Equations Turbulent kinetic energy: Potential temperature fluctuations: Flux of potential temperature :
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Boundary Layer Height Momentum flux derived Heat flux derived
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Calculation
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vs. vs.
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Total Budget Equations Turbulent kinetic energy: Potential temperature fluctuations: Flux of potential temperature :
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vs. vs.
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Temperature Forecasting Curve Forecasting Curve
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Anisotropy vs.
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