Vortices and tornado in mesoscale turbulence theory: a numerical pattern of 3D tornado rise

Category: 15-2
V.N. Nikolaevskiy, A.Yu. Gubar



UDC 551.517



V.N. Nikolaevskiy, A.Yu. Gubar


Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia


Abstract. The concept of homogeneity in turbulence is extended to the case of constant mean velocity gradient. This approach is relevant to a stratified atmosphere and differential volumes in any continuum model. The basic ideas of A.N. Kolmogorov for such a situation are recalled. It is shown that they are in full accordance with the possibility to introduce the angular velocity pseudo-vector as internal parameter for thermodynamically open turbulent system if its scale exceeds mesovortex size.

            The continuum description is formulated within the standard Cauchy's approach to the tensor of stresses averaged over cross-sections of the representative space cell. The possible asymmetry of the tensor is a consequence of the angular moment balance of the mesovortices. As the result, the effective 3D + time nonlinear equation set is developed. The suggested solution describes the tornado generation from a cloud of initial vortices. The dependence of turbulent rotation viscosity on spin vortex velocity permits to localize the tornado body due to the nonlinear diffusion effect.

            Numerical calculations were performed at two different clusters using Parjava program environment. The growth of a typical tornado structure, including secondary mesovortexes, rotating inside the tornado eye wall, is shown in a sequence of pictures. Their visual comparison with the Isabel hurricane (12–13.09.2003) is represented. 

Keywords: tornado, vortices, turbulence, angular momentum, scaling.



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