In What Sense Is Turbulence an Unsolved Problem?

Abstract

Turbulence can be narrowly defined as a property of incompressible fluid flow at very high Reynolds number, and thus an attempt can be made to specify what is and what is not understood about it. The applicability of the Navier-Stokes equations of hydrodynamics to real turbulent flows and the successes and limitations of direct numerical simulation are considered. A discussion is presented of universality, and mention is made of the remarkable success of Kolmogorov's 1941 scaling ideas despite uncertainties about basic underlying assumptions such as local isotropy. Extensions of this scaling to the multifractal picture of dissipation fluctuations are discussed, but this picture remains phenomenological. Turbulence as defined above remains "unsolved" in the sense that a clear physical understanding of the observed phenomena does not exist.