Ave.\
    St. Paul, MN 55105\
    U.S.A.
author:
- Pavel Bělík
- Brittany Dahl
- Douglas Dokken
- 'Corey K. Potvin'
- Kurt Scholz
- Mikhail Shvartsman
bibliography:
- 'tornado.bib'
title: 'Possible Implications of Self-Similarity for Tornadogenesis and Maintenance'
---

[^1]

Introduction {#sec:intro}
============

Power laws with a particular scaling exponent arise when a phenomenon “repeats itself on changing scales” [@mandelbrot83; @barnsley88; @barenblatt96; @barenblatt03]. This property is called self-similarity. We propose that the study of strong atmospheric vortices requires further exploration of their self-similarity, since self-similarity can point to important properties of the underlying dynamics. As will be shown, tornadoes appear to exhibit local self-similarity suggesting fractal phenomena and that will be the focus of this paper. A possible way tornadoes and mesocyclones might acquire self-similarity is through a vortex sheet roll-up; this process would give rise to the hypothesized vorticity and velocity power laws discussed below.

Self-similarity can manifest itself in several ways in atmospheric flows. One such manifestation is scale-invariance of some characteristic of the flow, which may be demonstrated by the existence of a power law for the characteristic. Examples include the scenarios discussed below, where power laws for vorticity/pseudovorticity or velocity are hypothesized [@wurmangill00; @wurmanalexander05; @cai05].

Self-similarity 