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. We find two bottleneck phenomena: While the local scaling exponent zeta r(r) of the structure function decreases monotonically, the local scaling exponent zeta p(p) of the corresponding spectrum has a minimum of zeta p(pmin) ~ 0.45 at pmin ~ (10 eta )-1 and a maximum of zeta p(pmax) ~ 0.77 at pmax ~ 8L-1. 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.