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

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.

arXiv comment31 pages including appendices, 10 figures

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• Sudden relaminarisation and lifetimes in forced isotropic turbulence
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• Self-organization and transition to turbulence in isotropic fluid motion driven by negative damping at low wavenumbers
• Qian Jian and His Contribution to Small-Scale Turbulence Studies
• The infinite Reynolds number limit and the quasi dissipative anomaly
• Does intermittency affect the inertial transfer rate in stationary isotropic turbulence?
• Critical transition to a non-chaotic regime in isotropic turbulence