Numerical Pattern of 3D Tornado Rise with Account for Mirror Asymmetry

Abstract

Authors are returning to the basic concepts of turbulence – homogeneity and symmetry principles. It is shown that the homogeneity in the sense of constant mean velocity gradient (instead of constant velocity) permits to introduce mirror asymmetry. This way is corresponding to stratified atmosphere and to differential volume in any continuum model. The basic ideas of A. N. Kolmogorov do not contradict to such an approach. Moreover, the use of the intrinsic eddy angular velocity (so-called spin or mesovorticity) as the internal thermodynamic parameter becomes necessary for adequate description of tornado (and intensive atmospheric vortices, in general) dynamics. The continuum description is formulated with standard introducing of stresses averaged over a cross-section, and now motivated asymmetry leads to the vortices moment of momentum balance. The set of nonlinear 3D partial differential equations is suggested for the problem of tornado generation from a cloud of initial vortices. The dependence of turbulent rotation viscosity on the spin permits to localize the tornado body due to the nonlinear diffusion effect. Numerical calculations are performed at two different clusters using Parjava program environment. The growth of typical tornado structure is shown by a sequence of pictures. A visual comparison with the Hurricane Isabel, 2003, is represented.