What Is a Vortex Filament?

Constant Vortex Strength

• In a fluid situation, a vortex line circulates consistently; in other words, the motion does not change in an ideal state. Because of the real-world effects of viscosity, though, the vortex will break down over time, coming to resemble a tornado. The stronger end is on the ground; as it goes up into the air, it diffuses as it widens,

Infinite Length

• Again, in a vacuum, a vortex would not end unless it hit a boundary. However, the action of air and fluid allow the vortex to widen on one end; again, imagine a tornado. The ground acts as a boundary; the unbounded end just loses cohesion and opens up.

Biot-Savart Law

• If you've ever been near a tornado, you know that the vortex inside it generates a considerable amount of velocity. The formula for this, for a two-dimensional case, is:

  velocity = circulation/2*pi*r,

  where r is the radius of the vortex. In a three-dimensional vortex, however, some calculus is required: the velocity equals the integral of circulation times radius over the absolute value of the radius raised to the third power, all divided by 4*pi.

Inertia

• As with many objects on the earth, vortices also follow the principles of inertia. In other words, if one vortex creates a flow in a certain direction, any ancillary vortices that spring up in that vortex's wake will follow it.