Dissipative distinctions

What is it about?

There have been numerous studies concerning the possibility of self-similar scaling laws in fully developed turbulent shear flows, driven over the past half-century or so by the early seminal work of Townsend (1956, The Structure of Turbulent Shear Flow. Cambridge University Press). His and nearly all subsequent analyses depend crucially on a hypothesis about the nature of the dissipation, e, of turbulence kinetic energy, k. It has usually been assumed (sometimes implicitly) that this is governed by the famous Kolmogorov relation  e=Ck^(3/2)/L, where L is a length scale of the energy-containing eddies and C is a constant. The paper by Dairay et al. (J. Fluid Mech. vol. 781, 2015, pp. 166–195) demonstrates, however, that, in the specific context of an axisymmetric wake, there can be regions where  has a different behaviour, characterised by a C that is not constant but depends on a varying local Reynolds number (despite the existence of a -5/3 region in the spectra). This leads to fundamentally different scaling laws for the wake.

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