Boltzmann-Jaynes variational method and the temperature distribution of thermals in the turbulent convective atmospheric surface layer

A statistical mechanism that explains the formation of probability distribution functions of thermals according to temperature fluctuations is considered. In the proposed approach based on the Boltzmann-Jaynes variational method, a statistical ensemble of convective thermals is characterized by a class of stationary probability densities that depend on temperature fluctuations. It is assumed that the probability density functions of this class may depend on the potential energy, as well as on the available potential energy. For a class of stationary probability density functions, the entropy functional is defined to be an analogue of the Boltzmann H-entropy. The equilibrium distributions of thermals according to temperature fluctuations correspond to the most probable distributions that yield a maximum of the entropy functional. The exponential and normal distributions of thermals according to temperature fluctuation that are constructed using the variational method quite adequately approximate field atmospheric observations, as well as the results of laboratory modeling.