| Summary: | Mathematical modeling is the most important tool for constructing the theory of concentrated tornado-like vortices. A review and analysis of computational and theoretical works devoted to the study of the generation and dynamics of air tornado-like vortices has been conducted. Models with various levels of complexity are considered: a simple analytical model based on the Bernoulli equation, an analytical model based on the vorticity equation, a new class of analytical solutions of the Navier–Stokes equations for a wide class of vortex flows, and thermodynamic models. The approaches developed to date for the numerical simulation of tornado-like vortices are described and analyzed. Considerable attention is paid to developed approaches that take into account the two-phase nature of tornadoes. The final part is devoted to the analysis of modern ideas about the tornado, concerning its structure and dynamics (up to the breakup) and the conditions for its occurrence (tornadogenesis). Mathematical modeling data are necessary for interpreting the available field measurements while also serving as the basis for planning the physical modeling of tornado-like vortices in the laboratory.
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