Scalings of scale-by-scale turbulence energy in non-homogeneous turbulence

Abstract

A theory of non-homogeneous turbulence is developed and is applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics and predicts power law scalings of second-order structure functions which have some similarities with but also some differences from Kolmogorov scalings. These scalings arise as a consequence of these assumptions, of the general inter-scale and inter-space energy balance and of an inner-outer equivalence hypothesis for turbulence dissipation. They reduce to usual Kolmogorov scalings in stationary homogeneous turbulence. Comparisons with structure function data from three qualitatively different turbulent wakes provide support for the theory's predictions but also raise new questions for future research.