THEORY OF TURBULENCE

This review is concerned with modern theoretical approaches to turbule nce, in which the problem can be seen as a branch of statistical field theory, and where the treatment has been strongly influenced by analo gies with the quantum many-body problem. The dominant themes treated a re the development (since the 1950s) of renormalized perturbation theo ries (RPT) and, more recently, of renormalization group (RG) methods. As fluid dynamics is rarely part of the physics curriculum, in section 1 we introduce some background concepts in fluid dynamics, followed b y a skeleton treatment of the phenomenology of turbulence in section 2 , taking flow through a straight pipe or a plane channel as a represen tative example. In section 3, the general statistical formulation of t he problem is given, leading to a moment closure problem, which is ana logous to the well known BBGKY hierarchy, and to the Kolmogorov -5/3 p ower law, which is a consequence of dimensional analysis. In section 4 , we show how RPT have been used to tackle the moment closure problem, distinguishing between those which are compatible with the Kolmogorov spectrum and those which are not. In section 5, we discuss the use of RG to reduce the number of degrees of freedom in the numerical simula tion of the turbulent equations of motion, while giving a clear statem ent of the technical problems which lie in the way of doing this. Last ly, the theories are discussed in section 6, in terms of their ability to meet the stated goals, as assessed by numerical computation and co mparison with experiment.