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

Abstract

The pseudospectral method, in conjunction with a technique for obtaining scaling exponents ζ_{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 analyzing experimental data. This method differs from the ESS technique, which plots S_{n}(r) against S_{3}(r), with the assumption S_{3}(r)∼r. Using our method for the particular case of S_{2}(r) we obtain the result that the exponent ζ_{2} decreases as the Taylor-Reynolds number increases, with ζ_{2}→0.679±0.013 as R_{λ}→∞. 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.