Material conservation of kinetic helicity density

The kinetic helicity conservation law impliesTherefore $q$ is materially constant exactly when the right side vanishes. Incompressible flow together with constancy of $w-u^2/2$ along vortex lines is sufficient. In compressible flow, the density-normalized quantity satisfies $D(q/\rho )/Dt=-(\mathbf{\omega }/\rho )\cdot \nabla (w-u^2/2)$.