The recently discovered non-equilibrium turbulence dissipation law implies the existence of axisymmetric turbulent wake regions where the mean flow velocity deficit decays as the inverse of the distance from the wake-generating body and the wake width grows as the square root of that distance. This behaviour is different from any documented boundary-free turbulent shear flow to date. Its existence is confirmed in wind tunnel experiments of wakes generated by plates with irregular edges placed

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... rmal to an incoming free stream. The wake characteristics of irregular bodies such as buildings, bridges, mountains, trees, coral reefs and wind turbines are critical in many areas of environmental engineering and fluid mechanics. As described in many turbulence textbooks, mean turbulence spatial profiles (e.g. mean flow and turbulence intensity profiles) are self-similar/self-preserving in far enough regions of many boundary-free turbulent shear flows, such as various turbulent wakes, jets and plumes. Turbulent flows are also archetypal dissipative phenomena and another property central to their understanding and modelling is the dissipation rate ε of turbulence kinetic energy K at high Reynolds number (a number representing the ratio between inertial and viscous forces). Tennekes & Lumley [1] refer to the widely known and used high Reynolds number assumption ε ∼ K 3 2 L (where L is an appropriate correlation lengthscale giving a measure of the large turbulent eddies) as "one of the cornerstone assumptions of turbulence theory". Other authors refer to this cornerstone assumption as the "zeroth law of turbulence" [2]. In particular, it is central to mean field theories of turbulent flows called Reynolds Averaged Navier-Stokes (RANS) models [3] and to coarse-graining approaches called Large Eddy Simulations (LES) [4]; and it is also an integral part of the Kolmogorov-Richardson phenomenology of turbulent spectral equilibrium [5] which has been a centrepiece in our understanding and modelling of smallscale turbulence since the 1940s (e.g. the estimate that the number of turbulent degrees of freedom is proportional to the 9/4 power of Reynolds number relies on ε ∼ K 3 2 L). One important way in which the zeroth law is key is its pivotal role in determining the scaling laws of selfsimilar/self-preserving free shear turbulent flow profiles. As shown by George [6], these profiles are obtained from the average momentum equation (with neglected viscous force as the Reynolds number is high), the kinetic energy equation and an assumption on dissipation. These two equations determine the streamwise evolutions of the self-similar/self-preserving mean flow and kinetic energy profiles in the plane normal to the streamwise direction. Whilst the mean flow U is shaped by the turbulence via the turbulent (Reynolds) stress R, also assumed self-similar/self-preserving, the spatial dependence of the kinetic energy K is shaped by the effects of turbulent production P, transport T and dissipation ε, all of which are assumed self-similar/self-preserving too. This procedure is not conclusive, however, without an assumption on the dissipation, and this is where the zeroth law is key [6] . Work over the past six years has revealed the existence of regions in the lee of both fractal and regular grids where a new high Reynolds number dissipation law holds [7] [8] [9] [10] [11] [12] , different from ε = C ε K 3 2 L with C ε independent of Reynolds number. In these regions, C ε ∼ Re m G Re n L where n and m are both close to 1, Re G is a global Reynolds number based on inlet/boundary conditions and Re L is a local Reynolds number based on local velocity and length scales. Re L decays with streamwise distance from the turbulence-generating grid in these regions which were termed non-equilibrium regions by [10] in the expectation that the rate of nonlinear energy transfer across length-scales does not balance dissipation as the new dissipation law strongly suggests a non-Richardson-Kolmogorov cascade [8] . In most boundary-free turbulent shear flows (plane wakes, mixing layers, jets and plumes) the local Reynolds number does not decrease with increasing streamwise distance from the source [1]. A notable exception of great engineering, environmental, geophysical and scientific importance is the axisymmetric turbulent wake [1]. As the non-equilibrium regions discovered to date are regions where the local Reynolds number decreases with distance from various types of grids, we make the assumption in this work that the non-equilibrium dissipation law may also exist in some regions of some axisymmetric wakes generated by objects which, like grids, combine wake-like with jet-like behaviours. Examples of such objects are the plates in figures 1(c), 1(d) and 1(e). We may expect such non-axisymmetric plates to have axisymmetric mean wakes far enough downstream as