Experimental verification of the model dependence of the turbulent Prandtl number on the gradient Richardson number
V.A. Banakh, I.N. Smalikho, I.V. Zaloznaya
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: structural constant of temperature fluctuations, dissipation rate of the kinetic energy of turbulence, turbulent Prandtl number, gradient Richardson number
Abstract
A formula has been derived which connects the structural constant of temperature fluctuations with the dissipation rate of the kinetic energy of turbulence not through the turbulent thermal diffusivity, but through the vertical gradients of average wind speed and air temperature and the turbulent Prandtl number. To estimate the structural characteristics of temperature using this formula, we suggest a model based on the generalization of known data on the turbulent Prandtl number as a function of the gradient Richardson number. It has been experimentally shown that the time series of the structural constant of temperature, which is calculated using the proposed formula and independently found from the spectra of temperature fluctuations based on measurements of wind speed and air temperature with sonic anemometers at two altitudes, are consistent with each other. This confirms the correctness of the theoretical constructions, which serve the basic for the model dependence of the turbulent Prandtl number on the gradient Richardson number.
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