Abstract
The evolution of the sets where the velocity of a Newtonian fluid exceeds a certain amount is studied by means of some integral identities deduced from the Navier–Stokes equations. It is found that in addition to the viscous diffusion of the velocity and the influence of the forcing, the velocity direction plays an important role: the more rapidly this direction varies, the quicker the region and the velocity within it will decrease. Since turbulent flows tend to change directions abruptly, this may be regarded as an instance of turbulence-enhanced dissipation.