Daniel Silverstein
December 14, 2007

(Submitted as coursework for Physics 210, Stanford University, Fall 2007)

Fig. 1: A super-cell thunderstorm was divided into three parts by Dr. Fujita: The cloud wall, cloud collar, and tail cloud. Tornadoes typically rotate cyclonically about the wall cloud.

The Anatomy of a Tornado

A tornado is a violently rotating column of air, a powerful force of a nature, which is well known throughout the United States where they are most common. Strong tornadoes can cause immense structural damage and even threaten lives. They can maintain wind speeds from 100-300mph, travel for miles, and become nearly a mile wide.

In the late 1950s, Dr. Fujita began his studies of tornadoes and thunderstorms. He proposed the first qualitative ranking system for tornadoes (f0-f5), based on wind speed and damage caused [1]. Dr. Fujita also first proposed the tornado lifecycle: beginning with a dropping stage, then a rounded bottom stage, and ending with a shrinking stage [1]. Observational studies have shown that the most powerful tornadoes (f4-f5) are generated almost exclusively by super-cell thunderstorms (see fig. 1) [4]. The terms wall cloud, tail cloud, and collar cloud were all coined by Dr. Fujita to better describe the super-cell thunderstorms [1]. When the wall cloud of a super-cell thunderstorm is rotating cyclonically, it is called a mesocyclone, and the mesocyclone is one of the best predictors of tornadoes. The mesocyclone can be seen directly with Doppler radar as a 'hook echo'. Though the number of deaths from tornadoes has decreased recently due to increased public awareness, a better understanding of tornadogenesis mechanisms can lead to better forecasting and warnings. [1].

Tornadogensis mechanisms

There are multiple theories for the details of the formation of strong tornadoes, but they all rely on the presence of a mesocyclone. Mesocylcones occur in areas of high horizontal wind shear. That is, areas where there is a dramatic change in wind speed with a change in height. The horizontal wind shear creates a horizontal vorticity, a row of rotating air. When the horizontal vorticity encounters an updraft, it is tilted, and becomes a vertically rotating column of air or vertical vortex (see fig. 2) [6]. Doppler radar data have confirmed that mesocylclones form around a strong updraft core [1].

The vertical vorticity present in the mesocyclone is one of two necessary components for the creation of the tornado. After the formation of the mesocyclone, all that is needed is for the vertical vorticity to stretch to ground level and intensify [6]. One mechanism for the dropping of the vorticity is a downdraft. The rear flank downdraft (RFD) model posits that the downdraft frequently present along the rear flank of a super-cell is responsible for sending the vorticity downwards (others have proposed a forward flank downdraft mechanism) [1]. Another model posits that the humidity being pulled into the mesocyclone from the tail cloud causes an increase in humidity (ie mass) which pulls the vertical vorticity downwards. However, this weakens the vorticity, which must then be strengthened by another updraft [1].

Fig. 2: Horizontal wind shear creates a horizontally rotating section of air. The vortex is then titled into the vertical axis via an updraft, becoming a mesocyclone.

Regardless of the mechanism of the stretching of the vertical vorticity, most models agree that there are a few factors which are integral to tornadogenesis. Studies and simulations have shown that near ground wind shear is proportional to tornado strength [3]. Strong tornadoes form almost exclusively in areas of high vertical wind shear and high convective available potential energy (CAPE). The CAPE has been shown to be a relevant measure for determining tornadogenesis because areas of convective inhibition impede tornadogenesis almost entirely [4]. It is the high wind shear and high CAPE which make mesocyclone formation most likely and thus tornadogenesis most likely [6].

Tornado Dynamics

Using the linear theory of dry, unstable flow in large shear, Davies-Jones showed that when the winds of a thunderstorm have a vertical component, then a vortex will be titled and mesocyclones will form, leading to tornadogenesis [9].

Here the perturbation of a particle from it's equilibrium state (w') is related to the vorticity ξ, where L is the linear material derivative operator. L = (d/dt +Vxd/dx+Vyd/dy).

Here η' is defined.

The streamwise velocity ωs is the storm wind velocity in the vertical direction, or the dot product between the velocity and the vertical unit vector. φ and ψ are angles relating the relation between the shear and the storm wind. Assuming ωs != 0, they find that:


Here the direction of the storm winds and the vorticity are in the same direction, and are related by a tittling factor. And so a vertical component of the storm winds leads to cyclonically rotating updrafts -- a mesocyclone.

Field Evidence

Initially, tornado observation involved pouring over photos to estimate wind speed and direction. In 1957, Dr. Fujita found the first evidence of a mesocyclone spawning a tornado after studying 150 pictures of a Fargo, ND tornado [1]. The pictures demonstrated a rotating cloud wall, indicative of a mesocyclone, before the formation of the tornado.

With the invention of the mobile doppler radar, tornado observation became a far more active and precise process. Observational studies by storm chasers in the late 1970's confirmed tornado formation by the RFD mechanism [5]. The VORTEX experiment was an extensive storm chasing endeavour performed in 1994 and 1995. The best data sets from that time period demonstrated that low level shear and low level cyclones were the best predictors of tornadogenesis [5]. A study of a strong Nebraska tornado (5/21/95) confirmed the existence of low level shear and a strong updraft immediately prior to the tornado formation [8]. A similar study of a Texas tornado outbreak (5/27/95) showed that all the tornadoes of magnitude greater than f1 were associated with pre-existing rotation in low levels. These tornadoes formed in close proximity to the storm boundaries where updrafts are stronger and longer lived. All the strong tornadoes were also associated with local maximums of the the vertical vorticity [2,6]. The soundings of 87 super cell thunderstorms in Alberta, Canada, showed that strong tornadoes were associated with large shear values. The presence of low level mesocyclones and high wind shear within 1km of the ground were found to be the best predictors of tornadogenesis [3]. Soundings of 518 super cell thunderstorms in the US from 2001-2003 demonstrated that tornadogenesis was suppressed in the presence of a region of convective inhibition, which would depress the titling of the vorticity [4].

© Daniel Silverstein. The author grants permission to copy, distribute and display this work in unaltered form, with attributation to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


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[9] R. Davies-Jones, "Streamwise vorticity: The Origin of Updraft Rotation in Supercell Storms," J. Atmos. Sci. 41 2991 (1984).