An overview of the effect of large-scale inhomogeneities on small-scale turbulence

The well-known isotropic relations [see Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 301 (1941); 32, 16 (1941); A. M. Yaglom, ibid. 69, 743 (1949)] between second-order and third-order structure functions are, in general, unlikely to be satisfied in turbulent flows encountered in the laboratory at moderate values of the Reynolds number. The main reason for this is the non-negligible correlation between the length scales at which the initial injection of turbulent energy occurs, those which dominate the transfer of this energy down the "cascade" and those which are responsible for dissipating this energy. In the majority of flows, there is a non-negligible inhomogeneity (sometimes nonstationarity) which may be caused by different physical phenomena. This paper presents an overview of how the equations of Kolmogorov and Yaglom can be "generalized" to provide a more realistic description of small-scale turbulence. The focus is mainly on locally isotropic regions of the flow, investigated using one-point measurements and Taylor's hypothesis. We are concerned principally with decaying grid turbulence, for which several results have already been obtained, but other flows, e.g., fully developed channel and jet flows, are also discussed.