Critical exponents and universality in fully developed turbulence

A new perspective on the critical phenomena aspects of fully developed turbulence (FDT) is considered. The energy (or enstrophy) dissipation rate epsilon (or tau) is pointed out to be the suitable quantity to be identified as the order parameter for the FDT problem. Multi-fractal model has been used to provide a detailed structure for the critical exponent sigma associated with this order parameter that appears to exhibit an interesting universality covering radically different FDT systems in fluid and plasma dynamics. This result also appears to provide a consistent framework for classification of dissipation field into critical, subcritical and supercritical cases. Some FDT problems that exemplify these cases are discussed. This classification is validated further by considering the probability density functions (PDF) of relevant flow-variable gradients in the FDT problems exemplifying the various cases. (c) 2005 Elsevier Ltd. All rights reserved.