A new method of identifying self-similarity in isotropic turbulence

Abstract

In order to analyse results for structure functions, $S_n(r)$, we propose plotting the ratio $|S_n(r)/S_3(r)|$ against the separation $r$. This method differs from the extended self-similarity (ESS) technique, which plots $S_n(r)$ against $S_3(r)$, where $S_3(r)\sim r$. Using this method in conjunction with pseudospectral evaluation of structure functions, 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 ${\zeta }_2\to 0.67\pm 0.02$ 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.