Universality of rare fluctuations in turbulence and critical phenomena

Abstract

A statistical treatment of three-dimensional turbulent flow continues to pose a challenge to theorists1,2. One suggestion invokes an analogy with equilibrium phase transitions3. Here we approach this idea experimentally, presenting evidence of a strong analogy between the statistical behaviour of a confined turbulent flow andthat of a model of the critical behaviour of a ferromagnet. Both systems experience large fluctuations limited only by the system size. We find that the power consumption measured in turbulent-flow experiments and the magnetization at the critical point of the ferromagnet have probability distributions of the same functional form, irrespective of Reynolds number on the one hand and system size on the other. The distributions both have non-gaussian tails that characterize the large-amplitude fluctuations. In this region, the scaled distributions for the two systems collapse onto a single universal curve over at least four orders of magnitude. This suggests a basic similarity in the finite-size corrections to the fluctuation statistics in the limit of infinite system size (for the magnetic system) or infinite Reynolds number (for turbulent flow).