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.

9 pages, 3figures on request

References in corpus (5)

• Far Dissipation Range of Turbulence
• 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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