Experimental Verification of the Model Dependence of the Turbulent Prandtl Number on the Gradient Richardson Number

Abstract

A formula has been derived which connects the structural constant of temperature fluctuations with the dissipation rate of kinetic energy of turbulence not through the turbulent thermal diffusivity but through the vertical gradients of average wind velocity and air temperature and the turbulent Prandtl number. To estimate the structural constant of temperature using this formula, a model based on generalization of known data on the turbulent Prandtl number as a function of the gradient Richardson number is proposed. 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 velocity and air temperature with sonic anemometers at two altitudes, are consistent with each other. This confirms correctness of the theoretical constructions the generalized results of which serve as the basis for the model dependence of the turbulent Prandtl number on the gradient Richardson number and opens possibilities of remote determination of the structural constant of temperature from measurements of wind velocity and temperature.