Far-dissipation range of turbulence

Abstract

Navier-Stokes turbulence at low Reynolds number (${\mathit{scrR}}_{\lambda }$≊15) is studied by high-resolution computer simulation. The energy spectrum in the range 5${\mathit{k}}_{\mathit{d}}$<k<10${\mathit{k}}_{\mathit{d}}$ is well fitted by ${\mathit{k}}^{\mathrm{\alpha }}$exp(-ck/${\mathit{k}}_{\mathit{d}}$), where ${\mathit{k}}_{\mathit{d}}$ is the Kolmogorov dissipation wave number, α≊3.3 and c≊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 α=3, c≊11.