Stability

This page is utterly incomplete. I'm working on it.

A tornado vortex is simply a structure built of fluid. How does it remain stable and resist being dissipated immediately? The animation loop that began this web page shows a tornado vortex that is perturbed at its base and propagates disturbances as waves along its axis. The disturbance propagates along the tornado, but the tornado returns basically to its previous form. In this sense it is a stable feature. Many people have observed tornadoes with bulges or constrictions that propagate up them.

The air flow in which it is embedded carries a tornado funnel with it and draws it into all sorts of wild shapes sometimes -- shapes like arches and lariats. Yet, the vortex persists.

Even though there is no mechanism that can make a Rankine vortex in the atmosphere, it makes a simple model with which to analyze stability.

Stability comes from restoring forces that return a vortex to its original form no matter how it is deformed. The graphic below shows how the rankine vortex supplies these forces. The two forces in question are...

When these two forces are in balance air simply orbits around the vortex axis without there being any effective means of accelerating this rotation. That is, the Rankine vortex just spins like a solid body. The graphic shows three segments of the vortex. The larger segments are at the equilibrium size of the vortex. Suppose that the pressure inside the vortex drops slightly and the middle segment attempts to shrink as a result. Because air cannot flow into the vortex from the outside without first increasing the spin of the vortex, air above and below this segment within the vortex will flow into it to expand the segment back to equilibrium. The opposite occurs if pressure inside the vortex tries to expand it beyond equilibrium. Now, assume that the middle segment manages to shrink by some other means. In order to maintain its circulation, the smaller segment will have to spin faster. The centrifugal acceleration either exceeds the pressure force, which forces the segment to expand again, or the central pressure will have to decrease, which will draw air from above and below to expand it again. The vortex may send disturbances up and down its length, but it maintains its shape and size well.

Evolution

Even though a vortex is rather stable, the tornado evolves in a typical way as it intensifies and then dies. According to Robert P. Davis-Jones the typical life evolution of a tornado is as follows.

A few very intense tornadoes decay quite abruptly by spreading out and becoming diffuse. It is possible in these cases that conditions of ambient rotation and suction in an updraft make a sustained, stable vortex impossible. For instance, if the updraft is very strong, and ambient rotation is weak, the inflowing air may attain enough momentum that it will flow beyond the equilibrium size of the rankine vortex. Now the surface pressure may be so low that it decelerates the updraft and brings the whole process to a halt. Then again, in this same situation, the vortex may become so small that eddy viscosity causes it to diffuse rapidly, or perhaps the eddies may assume a form that, instead of transfering momentum into the core of the vortex (Starr's hypothesis) they transfer it out.

The tornado also has a progression of typical forms that it assumes as it becomes increasingly intense. Much of this evolution is suggested by laboratory experiments and computer simulations, not all of it has been observed directly on real tornadoes. The following list explains the evolution. I compiled it from Neil B. Ward's summary of laboratory experiments (J. Atmos. Sci. 29, 1194-1204, 1972) and J.T. Snow's compilation of computer simulations (Rev. Geophy. and Space Phys. 20, 953-964, 1982). It is organized in terms of increasing maximum intensity in the mature state.

This drawing shows an intense parent vortex above with a downdraft in its core. The interaction of the downdraft with the ground surface increases the diameter of the vortex at its base, and causes it to degenerate into a family of three, smaller, but more intense vortexes, which T. Fujita once refered to as "suction spots." The family orbit around on a stagnant ring (SSR) where air diverging from the downdraft meets air drawn into the vortexes along the three jet inflows. The family of vortexes is usually compact, however, Ward suggested that the Newton, Kansas tornado of May 24, 1963, with its puzzling observations of multiple tornadoes moving in different directions, could be explained as a family of such multiple vortexes expanded out to a stagnant ring diameter of 1 mile.


Several images on this page are found at the web site of Wm. T. Hark. You can get more info and better resolution pictures there.

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