Helicity

this page is about helicity in fluid mechanics. For helicity of magnetic fields, see magnetic helicity).

In fluid mechanics, helicity is the extent to which corkscrew-like motion occurs. If a parcel of fluid is moving, undergoing solid body motion rotating about an axis parallel to the direction of motion, it will have helicity. If the rotation is clockwise when viewed from ahead of the body, the helicity will be positive, if anticlockwise, it will be negative.

Formally, helicity is defined as

$H=\int{\mathbf u}\cdot\left(\nabla\times{\mathbf u}\right)\,d^3{\mathbf r}.$

The concept is interesting because it is a conserved quantity: $H$ is unchanged in a fluid obeying the incompressible Navier-Stokes equations.

Helicity is a useful concept in theoretical descriptions of turbulence.

Categories: Fluid dynamics