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Possible implications of self-similarity for tornadogenesis and maintenance

1 Department of Mathematics, Statistics, and Computer Science, Augsburg University, Minneapolis,MN 55454, USA
2 Cooperative Institute for Marine and Atmospheric Studies, University of Miami, andNOAA/Atlantic Oceanographic and Meteorological Laboratory/Hurricane Research Division,Miami, FL, USA
3 Department of Mathematics, University of St. Thomas, St. Paul, MN 55105, USA
4 Cooperative Institute for Mesoscale Meteorological Studies, and School of Meteorology, Universityof Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, OK, USA

Topical Section: Mathematical Analysis in Fluid Dynamics

Self-similarity in tornadic and some non-tornadic supercell flows is studied and power lawsrelating various quantities in such flows are demonstrated. Magnitudes of the exponents in these powerlaws 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 fromradar observations and from numerical simulations, the tangential velocity, and the energy spectrum asa function of the wave number. Power laws for the vertical vorticity, pseudovorticity, and tangentialvelocity obtained from radar observations studied in the literature are summarized. Further support isgiven to the existence of a power law for vorticity by the analysis of data obtained from a numericalsimulation of a tornadic supercell. A possible explanation for an increase in vorticity in a developingtornado is provided, as well as an argument that tornadoes have approximate fractal cross sections andnegative temperatures. A power law that relates the increase of the approximate fractal dimension ofthe cross section of a negative temperature vortex to its energy content is derived, and the possibleapplicability of the box-counting method to determine this quantity from suitable radar images isdemonstrated.
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Keywords tornado; tornadogenesis; power laws; self-similarity; fractal; fractal dimension; vorticity; pseudovorticity; energy spectrum

Citation: Pavel Bělík, Brittany Dahl, Douglas Dokken, Corey K. Potvin, Kurt Scholz, MikhailShvartsman. Possible implications of self-similarity for tornadogenesis and maintenance. AIMS Mathematics, 2018, 3(3): 365-390. doi: 10.3934/Math.2018.3.365


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