Effect of finite Reynolds number on self-similar crossing statistics and fractal measurements in turbulence

Abstract

Stochastic simulations are used to create synthetic one-dimensional telegraph approximation (TA) signals based on turbulent zero crossings, where the interval between crossings is governed by a power law probability distribution with exponent $\alpha$. The power law exponent is determined for statistics of simulated TA signals, namely the box-counting fractal dimension $D_1$, energy spectrum exponent ${\beta }_{TA}$, and an intermittency exponent ${\mu }_{TA}$. For the binary TA signal with no variability in amplitude, the parameters are related linearly as $D_1=2-{\beta }_{TA}=1-{\mu }_{TA}$. The relations are unchanged if the crossing interval distribution has a finite power law region (i.e. inertial subrange) representing a flow with finite Reynolds number. However, the finite distribution yields statistics that are not truly scale-invariant, and distorts the linear relation between the statistic exponents and $\alpha$. The behavior is due to finite-size effects apparent from the survival function, or the complementary cumulative distribution, which for finite Reynolds number is only approximately self-similar and has an effective exponent differing from $\alpha$. An expression presented for the effective exponent recovers the expected relations between $\alpha$ and the TA statistics. The findings demonstrate how a finite Reynolds number can affect indicators of self-similarity, fractality, and intermittency observed from single-point measurements.

New version (including updated title) to be published in Physical Review Fluids. No changes were made to the results or key conclusions from the original version

References in corpus (3)

• Persistence Problem in Two-Dimensional Fluid Turbulence
• "Clusterization" and intermittency of temperature fluctuations in turbulent convection
• Persistence analysis of velocity and temperature fluctuations in convective surface layer turbulence

Cited by in corpus (2)

• Self-similar geometries within the inertial subrange of scales in boundary layer turbulence
• Stochastic modelling of the instantaneous velocity profile in rough-wall turbulent boundary layers