Universality of rare fluctuations in turbulence and critical phenomena

A statistical treatment of three-dimensional turbulent now continues to pos e a challenge to theorists(1,2). One suggestion invokes an analogy with equ ilibrium phase transitions(3). Here we approach this idea experimentally, p resenting evidence of a strong analogy between the statistical behaviour of a confined turbulent now and that of a model of the critical behaviour of a ferromagnet. Both systems experience large fluctuations limited only by t he system size. We find that the power consumption measured in turbulent-no w experiments and the magnetization at the critical point of the ferromagne t have probability distributions of the same functional form, irrespective of Reynolds number on the one hand and system size on the other. The distri butions 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 magnitu de. This suggests a basic similarity in the finite-size corrections to the fluctuation statistics in the Limit of infinite system size (for the magnet ic system) or infinite Reynolds number (for turbulent how).