Department/School

Mathematics

Date

1-1-2018

Document Type

Article

Keywords

tornado, tornadogenesis, power laws, self-similarity, fractal, fractal dimension, vorticity, pseudovorticity, energy spectrum

DOI

https://doi.org/10.3934/Math.2018.3.365

Abstract

Self-similarity in tornadic and some non-tornadic supercell flows is studied and power laws relating various quantities in such flows are demonstrated. Magnitudes of the exponents in these power laws are related to the intensity of the corresponding flow and thus the severity of the supercell storm. The features studied in this paper include the vertical vorticity and pseudovorticity, both obtained from radar observations and from numerical simulations, the tangential velocity, and the energy spectrum as a function of the wave number. Power laws for the vertical vorticity, pseudovorticity, and tangential velocity obtained from radar observations studied in the literature are summarized. Further support is given to the existence of a power law for vorticity by the analysis of data obtained from a numerical simulation of a tornadic supercell. A possible explanation for an increase in vorticity in a developing tornado is provided, as well as an argument that tornadoes have approximate fractal cross sections and negative temperatures. A power law that relates the increase of the approximate fractal dimension of the cross section of a negative temperature vortex to its energy content is derived, and the possible applicability of the box-counting method to determine this quantity from suitable radar images is demonstrated.

Published in

AIMS Mathematics

Citation/Other Information

Bĕlík, P., Dahl, B., Dokken, D., Potvin, C. K., Scholz, K. & Shvartsman, M. M. (2018). Possible implications of self-similarity for tornadogenesis and maintenance. AIMS Mathematics, 3(3), 365–390. https://doi.org/10.3934/Math.2018.3.365

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