Scale averaged trends of dissipation and enstrophy in fluid turbulence

Fluid turbulence is typically characterized as a tangle of high enstrophy (vorticity squared), low pressure vortices, embedded in regions of straining motions which possess high kinetic energy dissipation. The intermittent statistics of enstrophy and dissipation, which quantify rotation and strain respectively, considered over inertial scales, are expected to approach one another, in the traditional paradigm of small-scale universality. Using a scale-based analysis of the Poisson equation that relates pressure, energy dissipation and enstrophy, obtained from the incompressible Navier-Stokes equations, we show that regions of high enstrophy and low dissipation are more prevalent than regions of low enstrophy and high dissipation. Consistent with this discrepancy is the finding that the intermittency exponents of local averages of enstrophy and dissipation differ by a finite amount at least up to Taylor micro-scale Reynolds number, R_λ = 1300, and that these differences can be attributed to the non-trivial pressure laplacian contributions.