Beyond self-similarity in homogenous turbulence

The idea that homogenous turbulence follows a self-similar evolution when it is freely decaying is not new in the turbulence literature (see for instance George PoF 1992). However, self-similarity is generally accepted to be valid (if at all) far from initial conditions, i.e. several turnover times after the onset of decay. At earlier times, self-similarity is less likely to be valid, as the flow evolution strongly depends on its initial conditions and flow history, rather than exclusively on "local" flow physics. Currently, no concrete theoretical framework exists for the description of this early non self-similar evolution, which exhibits important phenomena, as for instance a universal non-classical dissipation scaling (see Vassilicos ARFM 2015). In this talk, I will present a theoretical and numerical (DNS) analysis of this early-stage evolution of turbulence. I will derive non self-similar expressions for the various quantities of interest, and a non power-law decay equation for the turbulence kinetic energy. Contrary to the classical self-similar analysis, the various quantities are depedent on terms which express the influence of the initial conditions, and the departure of the flow from them.