Far-dissipation range of turbulence

Abstract

Navier-Stokes turbulence at low Reynolds number (${\mathit{scrR}}_{\ensuremath{\lambda}}$\ensuremath{\approxeq}15) is studied by high-resolution computer simulation. The energy spectrum in the range 5${\mathit{k}}_{\mathit{d}}$k10${\mathit{k}}_{\mathit{d}}$ is well fitted by ${\mathit{k}}^{\mathrm{\ensuremath{\alpha}}}$exp(-ck/${\mathit{k}}_{\mathit{d}}$), where ${\mathit{k}}_{\mathit{d}}$ is the Kolmogorov dissipation wave number, \ensuremath{\alpha}\ensuremath{\approxeq}3.3 and c\ensuremath{\approxeq}7.1. High-order spatial derivatives of the velocity field exhibit strong intermittency, associated with gentle spatial variation of large-scale structure rather than with sparse, intense small-scale structures. Analysis by the direct-interaction approximation, which ignores intermittency, gives \ensuremath{\alpha}=3, c\ensuremath{\approxeq}11.