Transport of turbulent vorticity increments

Starting with the Navier-Stokes equations, a transport equation is written for the sum of the squared vorticity increments in homogeneous isotropic turbulence. This equation is compared with that for the sum of the squared velocity increments; whereas the latter equation exhibits a linear dependence on separation, the former does not. In the limit of a negligibly small separation, the new equation expresses a balance between the production and dissipation of the mean square vorticity gradient. All terms in the equation have been measured using a three-component vorticity probe in the self-preserving region of a low Reynolds number turbulent wake.