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.