FAR-DISSIPATION RANGE OF TURBULENCE

Navier-Stokes turbulence at low Reynolds number (R(lambda) almost-equal-to 15) is studied by high-resolution computer simulation. The energy spectrum in the range 5k(d) < k < 10k(d) is well fitted by k(alpha) exp(-ck/k(d)), where k(d) is the Kolmogorov dissipation wave number, alpha almost-equal-to 3.3 and c almost-equal-to 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 alpha = 3, c almost-equal-to 11.