Bottleneck effects in turbulence: Scaling phenomena in r- versus p-space

Abstract

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 ${\zeta }_p(p_{min})\approx 0.45$ at $p_{min}\approx (10\eta {)}^{-1}$ and a maximum of ${\zeta }_p(p_{max})\approx 0.77$ at $p_{max}\approx 8L^{-1}$. 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.

arXiv comment9 pages, 3figures on request

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• Crossover from high to low Reynolds number turbulence
• Scale resolved intermittency in turbulence
• Universality in fully developed turbulence
• Finite size corrections to scaling in high Reynolds number turbulence

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