The function of the turbulent energy dissipation in the atmospheric surface layer
Authors: Voloshin V.G. , Kuryshina V.Yu. 
Published: November 2018

Introduction. The problem of energetics of atmospheric processes is one of the important problem in the modern meteorology. Distribution of the sources and sinks of energy, especially near the surface, also turbulent transport and transformation of energy reflect all features of the processes generated in the atmospheric boundary layer, their behavior and intensity.
Purpose. A purpose of the work is a description of processes of production of turbulent kinetic energy (TKE) and dissipation rate of TKE in the surface layer, because transition of heat energy into TKE and vice versa, occurs continuously in the presence of wind shift. These changes are reflected in the actual state of the surface layer, which is registered with the meteorological observations.
Investigation methods. On the basis of the assumption that the TKE dissipation rate is directly proportional to its production, an atmospheric surface layer model, including the surface layer parameterization based on the Monin-Obukhov similarity theory and the modified Businger relationships, is proposed. The model provides sufficiently accurate assessment of the energy conservation law both on the surface and in the air flux. Statistical features of atmospheric turbulence, such as the vertical gradients of substances, dispersion and covariance are universal functions of hydrostatic stability of the surface layer, therefore non-dimensional functions of TKE dissipation and smoothing of temperature inhomogeneity are determined from the TKE budget equation, which are given to a non-dimensional form.
Results. The dependence of dissipation from stratification and wind velocity over surfaces with different roughness is defined. Under unstable stratification the function of dissipation is greater than 1 (je>1) and in-creases with its growth, under stable stratification the function decreases to zero. If the conditions are close to neutral, the function form becomes an S-shape one. Under weak wind velocities (u £ 2m/s), the dissipation rate is small and does not exceed 5 cm2/c3. With increasing wind velocities, the stratification of layer tends to the neutral condition and the dissipation rate increases to 100-150 cm2/c3 depending on the surface roughness. The results are good consistent with the measurements, carried out for different stratifications and wind velocities.
A similar test of “closure” of the TKE budget equation is executed for the forces, representing the buoyancy effect. Ratio of the non-dimensional function of rate of smoothing of temperature inhomogeneity, jq, and temperature gradient, jT, is equal to 1 ((jq/jT)»1,0), that confirms satisfiability of all the energy budget equations for the surface layer, used in the proposed model.
Conclusion. The results are obtained not by observations, but by the atmospheric surface layer model, including all the energy budget equations, which provides execution of energy conservation law both on the surface and in the air flux. Standard meteorological observations contain information not only about meteorological parameters, representing the actual weather conditions, but also information about the surface layer scaling parameters, which allow to determine both the internal and sometimes external parameters of the surface layer and the atmospheric boundary layer.