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 nd two bottleneck phenomena: While the local scaling exponent r (r) of the structure function decreases monotonically, the local scaling exponent p (p) of the corresponding spectrum has a minimum of p (p min) 0:45 at p min (10) ?1 and a maximum of p (p max) 0:77 at p max 8L ?1. A physical argument starting from the constant energy ux 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.