Direct numerical simulation and theoretical analyses showed that the probability density functions (PDFs) of the energy dissipation rate and enstrophy in turbulence are asymptotically stretched gamma distributions with the same stretching exponent, and both the left and right tails of the enstrophy PDF are longer than those of the energy dissipation rate regardless of the Reynolds number. The differences in PDF tails arise due to the kinematics, with differences in the number of terms contributing to the dissipation rate and enstrophy. Meanwhile, the stretching exponent is determined by the dynamics and likeliness of singularities.

• Received 17 November 2022
• Revised 27 March 2023
• Accepted 30 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.254001