An ensemble of dynamically identical thermals and vertical profiles of turbulent moments in the convective surface layer of atmosphere

An ensemble of convective thermals is distinguished from the surface layer of penetrative turbulent convection over a heated horizontally uniform surface. For an isolated convective element, an integral model of a quasi-stationary spontaneous jet is proposed which admits an exact analytical solution. A simple statistical model is constructed for an ensemble of dynamically identical thermals. In this model, convective thermals ascend in a static environment, their dynamic parameters are described by the equations of an isolated quasi-stationary jet, and their diameters are stochastic. It is shown that the ensemble of thermals rising in a horizontally homogeneous environment forms surface-layer turbulent moments. The analytical relationships for higher turbulent moments of vertical velocity and temperature are compared with experimental data from the second to the forth order inclusive.