2 v 2 2 1 O ct 1 99 4 Bottleneck effects in turbulence : Scaling phenomena in r - versus p - space

We (analytically) calculate the energy spectrum corresponding to various experimental and numerical turbulence data analyzed by Benzi et al. [1]. We find two bottleneck phenomena: While the local scaling exponent ζr(r) of the structure function decreases monotonically, the local scaling exponent ζp(p) of the corresponding spectrum has a minimum of ζp(pmin) ≈ 0.45 at pmin ≈ (10η) and a maximum of ζp(pmax) ≈ 0.77 at pmax ≈ 8L. A physical argument starting from the constant energy flux in p–space reveals the general mechanism underlying the energy pileups at both ends of the p–space scaling range. In the case studied here, they are induced by viscous dissipation and the reduced spectral strength on the scale of the system size, respectively.