Enstrophy and dissipation must have the same scaling exponent in the high Reynolds number limit of fluidturbulence

Writing the Poisson equation for the pressure in the vorticity-strain form, we show that the pressure has a finite inertial range spectrum for high Reynolds number isotropic turbulence only if the anomalous scaling exponents $\mu$ and $\mu_{\omega}$ for the dissipation and enstrophy (squared vorticity) are equal. Since a finite inertial range pressure spectrum requires only very weak assumptions about high Reynolds number turbulence, we conclude that the inference from experiment and direct numerical siimulation that these exponents are different must be a finite range scaling result which will not survive taking the high Reynolds number limit.