The article is devoted to the theoretical investigation of atmospheric convection on the base of analytical, semi-analytical and numerical solving equations of deep and shallow convection. The studies conducted have allowed the following conclusions: the heat of convective turbulence is convective cell; convective cell is unstable to a finite-amplitude disturbances; stability of cells is determined by external model's parameters and decrease with time; complicated nature of convective turbulence is conditioned by interaction between cells resulting in their coagulation or destruction; the model accounts for only interaction of cells located over each other. This and a number of simplifications for setting up a problem make possible to construct the convective cells's distribution function depending on their sizes, existence time and large-scale parameters; there are three ierarchy levels of convective formations in atmosphere: small-scale convective turbulence, thermals and cumulus clouds, convective ensembles; rotation of convective cells causes their stability to increase by enhanced stability of rotating cells a relatively weak thermals and cumulus clouds transform to whirlwind or tornado; a tropical cyclones may be considered to be (with minor reservations) large-scale analog of whirlwind. In spite of essentially different sizes the space structure and mechanism of these phenomena has much in common, in particular, the type of circulation.

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