How does the spinning of a tornado affect its shape and the path of its movement? In severe
storms, a tornado causes the surrounding winds to blow fiercely. As a result, the strong
winds push the tornado along, hopefully in a nondestructive path. To understand weather
patterns during strong storms, meteorologists (both professional and amateur) can use the
motion of tornados to predict the direction of the overall storm. A similar approach is used
to model fluid motion in turbulent regimes. By studying the motion of small swirling eddies,
we can understand the general motion of the fluid.


Without the cost of real-life experiments, mathematical modeling of fluid turbulence can
allow engineers and scientists to predict and reduce the aerodynamic drag on an airplane or
an automobile, understand the flow of blood in the human heart, or decrease the amount of
pollutants produced by a combustion engine. Under suitable conditions, some fluid motion
is such that the velocity (the direction and speed of the fluid) at any given time and position
is not found to be the same when it is measured several times under seemingly identical
situations. Fluctuating motions of this kind are said to be turbulent. Turbulence is composed
of eddies or vortices (think of little tornados) that zigzag and whirl around the overall
direction of motion. The mathematical equations that govern fluid turbulence, called the
Navier-Stokes equations, are known and reasonably well understood, but they are extremely
difficult to solve except in rare instances. Even accurate numerical solutions cannot be
achieved for many realistic flows important to industrial applications.


One approach taken to understanding turbulence is the development of mathematical
models for the movement of vortex filaments. The vorticity of a fluid is a measure of how
much the fluid is rotating or spinning. A vortex filament is a thin tube created when the
fluid rotates or spins very intensely about a single curve. When a filament rotates it changes
the fluid movement around it. The induced motion of the fluid then transports the filament.
Therefore the evolution equation for a vortex filament depends on the fluid motion it has
created. The best example of a vortex filament is a tornado. The rotation of the tornado
about its axis causes the air around it to move quickly. The air motion causes high winds
that change the shape of the tornado and puts the tornado into motion along a path.