Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence

TL;DR

This paper introduces a new spectral analysis method for structure functions in forced isotropic turbulence, revealing that the second-order scaling exponent decreases with increasing Reynolds number, challenging previous ESS-based results.

Contribution

It proposes a novel technique for extracting scaling exponents from structure functions, differing from ESS, and demonstrates its application to turbulence data, highlighting finite-viscosity effects.

Findings

The exponent ζ₂ decreases as Reynolds number increases.

The new method accounts for forcing effects exactly.

Results oppose previous ESS-based findings.

Abstract

The pseudospectral method, in conjunction with a new technique for obtaining scaling exponents $\zeta_n$ from the structure functions $S_n(r)$, is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio $|S_n(r)/S_3(r)|$ against the separation $r$ in accordance with a standard technique for analysing experimental data. This method differs from the ESS technique, which plots $S_n(r)$ against $S_3(r)$, with the assumption $S_3(r) \sim r$. Using our method for the particular case of $S_2(r)$ we obtain the new result that the exponent $\zeta_2$ decreases as the Taylor-Reynolds number increases, with $\zeta_2 \to 0.679 \pm 0.013$ as $R_{\lambda} \to \infty$. This supports the idea of finite-viscosity corrections to the K41 prediction for $S_2$, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.