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

Writing the Poisson equation for the pressure in the vorticity-strain form, it is shown that the pressure has a finite inertial range spectrum in the high Reynolds number limit of isotropic turbulence only if the anomalous scaling exponents μ and μω 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, it is concluded that the inference from experiment and direct numerical simulation that these exponents are different must be a finite-range scaling result which will not survive taking the high Reynolds number limit.