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Vladimir P. Lukin, Viktor V. Nosov, Oleg N. Emaleev, and Evgenii V. Nosov
SEMIEMPIRICAL HYPOTHESES OF THE TURBULENCE THEORY IN THE ATMOSPHERIC ANISOTROPIC BOUNDARY LAYER (FOR MOUNTAIN REGION) (Poster)

SEMIEMPIRICAL HYPOTHESES OF THE TURBULENCE THEORY IN THE ATMOSPHERIC ANISOTROPIC BOUNDARY LAYER (FOR MOUNTAIN REGION)


Vladimir P. Lukin, Viktor V. Nosov, Oleg N. Emaleev, and Evgenii V. Nosov
Institute of Atmospheric Optics SB RAS, Akademicheskii Ave.1, Tomsk, 634055, Russia


With the use of semiempirical hypotheses of the turbulence theory it was shown theoretically and experimentally that an arbitrary anisotropic boundary layer can be considered to be locally weakly anisotropic. For example, it is experimentally established that the turbulence behavior in the mountain boundary layer has significant anisotropy. As well known, the turbulence theory originates from the description of liquid and gas flows based on equations of hydrodynamics. The complete statistical description of random hydrodynamic fields is given by a characteristic functional. The characteristic functional contains information on endless ensemble of the field moments and satisfies the dynamic equation with functional derivatives. At present the acceptable methods of solutions are not found. At same time, for many practical problems it is enough to define only statistical moments of lower orders. Therefore the investigations in the turbulence theory are based traditionally on the set of Reynolds equations, which is the result of averaging of equations of hydrodynamics. However, in the set of Reynolds equations the number unknown values exceeds the number of equations. Closure of this set of equations is usually made by setting some relations between moments of hydrodynamic fields. The indicated relations found from the experiments or obtained from the physical considerations (for example, from considerations of dimensionality) are said to be semiempirical hypotheses of the turbulence theory. The main semiempirical hypotheses are usually reduced to setting the relationship between second moments of pulsations (deviations from the mean) of the velocity and the temperature and the averaged fields of the velocity and the temperature . These hypotheses are based, as a rule, on the analogy between turbulent and molecular motions. Therefore the terms can be considered as components of turbulent momentum fluxes and heat fluxes. A concept of the isotropic boundary layer (for plane-parallel flows) is not connected with the isotropy of hydrodynamic fields. In the isotropic layer there is a defined direction (the distance from the boundary plane), therefore the fields will not be isotropic. As is well-known, the outer scale of turbulence can be defined in different ways. For example, Tatarskii defines the vertical outer scale of turbulence L0T from the condition that the mean-square difference of random temperature values at two points is equal to its systematic difference. The outer scale of turbulence can be also defined from the deviation of the structure function of temperature fluctuations from the "2/3" law. In the Fourier-transform space, this scale corresponds to the scale L0V defined from the deviation of the one-dimensional spatial or temporal frequency spectra from the "5/3" law. There are also scales, which are the parameters in various theoretical models of the energy interval of the three-dimensional spectrum of fluctuations (for example, the Karman outer scale).


next up previous
Next: Attila Moór, Péter Ábrahám, Up: Session 1: Ground based Previous: Nicolas Lehner and J.
LESIA, Observatoire de Paris
2006-03-16