On a Scale-Invariant Criterion of Similarity for Rotating Flows
in Laboratory Modeling of Tornado-Like Vortices

S. G. Chefranov

Oboukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 119017 Russia
e-mail: schefranov@mail.ru

Received September 13, 2001; in final form, July 23, 2002

Abstract—The balance equation for the integral helicity of rotating flows is used to determine the sole scale-
invariant criterion of similarity for such flows, which is independent of the choice of the length and time scales.
This allows one to assess the adequacy of modeling real mesoscale atmospheric processes of tornado and helix
genesis on the scale of a laboratory setup, which accompany the evolution of tornado vortices. The estimated
dependence of the cross section of a tornado vortex on its height and intensity is consistent with empirical data.

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