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

TL;DR

This paper develops a theory for non-homogeneous turbulence in boundary-free shear flows, predicting power law scalings of structure functions that extend Kolmogorov's classical results, supported by experimental data.

Contribution

It introduces a novel theoretical framework with assumptions of inner and outer similarity, extending turbulence scaling laws beyond homogeneous conditions.

Findings

Predicted power law scalings of second-order structure functions.

Support from experimental data in turbulent wakes.

Raised new questions for future turbulence research.

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.