Review of developments in turbulence theory

Turbulence theory is difficult because the Navier-Stokes equations are an unclosed set of statistical relations. The review begins with an account of the problem of closure, and shows that this problem is evaded rather than solved by the methods now used for practical calculation: examples of the use of these methods are given. The bulk of the review is devoted to more fundamental procedures whose aim is to find the dependence of the pair correlation function on the separation of the two measuring points in space and time. This is done by making closure assumptions which are, at the least, free from arbitrary constants and which have some claim to uniqueness at the lowest level of complexity. The application of these theories to homogeneous isotropic turbulence is described. The review closes with an account of a problem in nuclear engineering which highlights both the defects of existing methods of calculation for turbulent flows, and the need for the better methods that the more fundamental procedures may one day offer.