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

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)/S₃(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 S₃(r), with the assumption S₃(r)∼r. Using our method for the particular case of S₂(r) we obtain the result that the exponent ζ₂ decreases as the Taylor-Reynolds number increases, with ζ₂ → 0.679±0.013 as R_λ→∞. This supports the idea of finite-viscosity corrections to the K41 prediction for S₂, 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.