Scaling of locally averaged energy dissipation and enstrophy density in isotropic turbulence

Using direct numerical simulations of isotropic turbulence in periodic cubes of several sizes, the largest being ${8192}^3$ yielding a microscale Reynolds number of $1300$, we study the properties of pressure Laplacian to understand differences in the inertial range scaling of enstrophy density and energy dissipation. Even though the pressure Laplacian is the difference between two highly intermittent quantities, it is non-intermittent and essentially follows Kolmogorov scaling, at least for low-order moments. Using this property, we show that the scaling exponents of local averages of dissipation and enstrophy remain unequal at all finite Reynolds numbers, though there appears to be a $\mathit{\text{very}}$ weak tendency for this inequality to decrease with increasing Reynolds number.