  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.
