Universality and scaling in fully developed turbulence

Abstract

The small scale velocity fluctuations in high Reynolds number incompressible fluid turbulence exhibit universal scaling properties independent of the large scale flow structures. The evidence for this universality and scaling from experiment and direct numerical simulation, which has considerably improved in recent years, is reviewed in this article. The emphasis is on those features which are independent of any particular statistical theory. Some attempt is made to link this phenomenological picture to Navier-Stokes dynamics, but this is necessarily quite incomplete since a fundamental theoretical understanding is still lacking.