Scaling and structure of extreme velocity gradients in turbulence

The formation of very localized and intense velocity gradients underlies intermittency in fully turbulent flows. While the typical value of velocity gradients scales with the Kolmogorov time scale τ_K, their fluctuations can be orders of magnitude larger and become increasingly intense as Reynolds number increases. Such extreme events play a crucial role in numerous applications, e.g. cloud physics, turbulent combustion, but a complete description still remains a major challenge. Using direct numerical simulations of isotropic turbulence with an unprecedented small-scale resolution, we characterize such extreme events over a wide range of Taylor-scale Reynolds numbers (R_λ). Specifically, by studying the PDFs of dissipation and enstrophy, we find that the extreme events scale as τ_K^-1R_λ^β, with β=0.775±0.025, weaker than β=1 predicted by existing theories. The observation that the velocity differences across very small distances can be as large as u_rms leads to the conclusion that the smallest length scale in the flow scales as ηR_λ^-α, with α=β-0.5, where η is the Kolmogorov length scale. Comparisons with the multifractal theory are also drawn. We further relate the exponent β<1 to the nonlocal stretching acting on a given vortex structure.