Progress in studying small-scale turbulence using 'exact' two-point equations

Abstract

The analytical framework based on the similarity hypotheses of Kolmogorov and Obukhov arguably provides an adequate description of homogeneous isotropic turbulence at very large Reynolds numbers. In the flows normally encountered in the laboratory, the Reynolds number is finite and other influences, for example those due to a mean shear or, more generally, inhomogeneities associated with the larger scales, are present. In this paper, we review and assess some of the current progress in using 'exact' two-point equations for analysing the manner in which small-scale turbulence is affected by different types of inhomogeneities that may be present. There is strong support for this approach from experimental and/or numerical data for decaying homogeneous isotropic turbulence and along the axis of a round jet where the Reynolds number remains constant. In each of these flows, the major source of inhomogeneity is the streamwise decay of energy. Overall implications are discussed in the context of results obtained in physical space, although the correspondence to the spectral domain is also commented on briefly.