Turbulence: Diffusion, Statistics, Spectral Dynamics

Abstract

It is probably a bit misleading to say that turbulent flow is “random”; even if the birth of an eddy out of an instability somewhere in the flow field is a matter of “chance,” its subsequent evolution must be governed by the Navier-Stokes equations. Being careful, we shall say no more than that the turbulence is chaotic, and that for many practical purposes it is sufficient to know something about the statistical properties of the flow field. However, there are circumstances in which a statistical treatment will not do. For example, in weather forecasting, we want to predict at what time a particular eddy will pass over a certain area, and at which stage in its life cycle.