Soliton theory of squall storms

Arsen'ev, S. A.; Shelkovnikov, N. K.

doi:10.3103/s0027134910050140

Cited by 4 publications

(11 citation statements)

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“…Figure 2a shows the meridional streamlines in the area where the tornado funnel is expanding [27]. Figure 2b illustrates the formation of a tornado near the Earth's surface [27] In [28], a mathematical model describing the process of formation of intense atmospheric vortices of the tornado type due to instability is constructed. The instability condition is an increase in the vertical component of the air velocity in the direction of the Earth's surface or an increase in the concentration of suspended particles.…”

Section: Simple Analytical Modelsmentioning

confidence: 99%

“…Such conditions can be realized in some cases in thunderclouds in the atmosphere and over the dusty or snow-covered surface of the Earth. The initial stage of tornado development is being studied in research [28].…”

Section: Simple Analytical Modelsmentioning

confidence: 99%

“…in [28] was considered to be known from observations. Then, in [28], an equation was constructed for the vertical component of vorticity:…”

Section: Simple Analytical Modelsmentioning

confidence: 99%

“…So, the density of the mixture of air and particles was equal ρ = ρ a (1 − Φ) + ρ p Φ. It should be noted that in order to conduct an analytical study, the vertical component of the velocity U z (x, y, z, τ) in [28] was considered to be known from observations. Then, in [28], an equation was constructed for the vertical component of vorticity:…”

Section: Simple Analytical Modelsmentioning

confidence: 99%

“…Further, in [28], an analysis of the equation obtained above for the vertical component of vorticity was conducted. For this, Equation (11) was presented in the form…”

Section: Simple Analytical Modelsmentioning

confidence: 99%

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Mathematical Modeling of Structure and Dynamics of Concentrated Tornado-like Vortices: A Review

Varaksin

Ryzhkov

2023

Mathematics

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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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Section: Simple Analytical Modelsmentioning

confidence: 99%

Section: Simple Analytical Modelsmentioning

confidence: 99%

“…in [28] was considered to be known from observations. Then, in [28], an equation was constructed for the vertical component of vorticity:…”

Section: Simple Analytical Modelsmentioning

confidence: 99%

Section: Simple Analytical Modelsmentioning

confidence: 99%

“…Further, in [28], an analysis of the equation obtained above for the vertical component of vorticity was conducted. For this, Equation (11) was presented in the form…”

Section: Simple Analytical Modelsmentioning

confidence: 99%

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