The invariant theory of isotropic turbulence

Abstract

The statistical theory of isotropic turbulence, initiated by Taylor (3) and extended by de Kármán and Howarth (2), has proved of value in attacking problems associated with the decay of turbulence. In its application to such hydro-dynamical problems, the theory falls into two parts, a kinematical part and a dynamical part. The kinematical aspect consists in setting up correlations between velocity components, or their derivatives, at two arbitrary points in the fluid, and reducing the form of the tensor thus obtained in accordance with the severely restrictive assumption of isotropic turbulence; the success of de Kármán and Howarth's investigations is largely attributable to their improved treatment of this purely kinematical problem. The dynamical part then consists in applying the implications of the equations of continuity and motion to the functions defining the correlation tensors, in order to obtain information concerning their functional dependence on time and on the displacement between the two points for which the correlations are computed.