Universality of intense velocity gradients in different turbulent flows

A central tenet of turbulence theory is the purported universality of flow properties at small scales. This has been thoroughly investigated and is now nominally well established for mean field quantities, such as the two-point correlation function (velocity spectrum). However, the small scales of turbulence are highly intermittent, as characterized by extreme fluctuations in velocity increments and gradients. In this study, we explore the universality of these extreme fluctuations. To that end, we analyze the statistical properties of velocity gradients from various flows, namely: homogeneous isotropic turbulence; turbulent channel flow at the center of the channel, both from direct numerical simulations, and von Karman mixing tank from laboratory measurements. Our comparison of various unconditional and conditional statistics across these different flows is consistent with universal properties for both mean and extreme events. Notably, the conditional average of strain on vorticity, which is crucial for understanding intermittency and its dependence on the Reynolds number, also shows consistent behavior. Our findings underscore the necessity of directly modeling velocity gradient dynamics as a critical component of turbulence modeling.