The role of initial conditions in affecting the evolution toward self-similarity of an axisymmetric turbulent jet is examined. The jet's near-field coherence was manipulated by non-circular exit geometries of identical open area, D 2 e , including a square and a fractal exit, for comparison with a classical round orifice jet. Hot-wire anemometry and 2D-planar particle image velocimetry experiments were performed between the exit and a location 26D e downstream, where the Reynolds stress profiles are self-similar. This study shows that a fractal geometry significantly changes the near-field structure of the jet, breaking up the large-scale coherent structures, thereby affecting the entrainment rate of the background fluid into the jet stream. It is found that many of the jet's turbulent characteristics scale with the number of eddy turnover times rather than simply the streamwise coordinate, with the entrainment rate (amongst others) found to be comparable across the different jets after approximately 3-4 eddies have been overturned. The study is concluded by investigating the jet's evolution toward a self-similar state. No differences are found for the large-scale spreading rate of the jets in the weakly self-similar region, so defined as the region for which some, but not all of the terms of the mean turbulent kinetic energy equation are self-similar. However, the dissipation rate of the turbulent kinetic energy was found to vary more gradually in x than predicted according to the classical equilibrium theories of Kolmogorov. Instead, the dissipation was found to vary in a non-equilibrium fashion for all three jets tested.

Tomographic particle image velocimetry experiments were conducted in the near and intermediate fields of two different types of jet, one fitted with a circular orifice and another fitted with a repeating-fractal-pattern orifice. Breda & Buxton (J. Vis., vol. 21 (4), 2018, pp. 525–532; Phys. Fluids, vol. 30, 2018, 035109) showed that this fractal geometry suppressed the large-scale coherent structures present in the near field and affected the rate of entrainment of background fluid into, and subsequent development of, the fractal jet, relative to the round jet. In light of these findings we now examine the modification of the turbulent/non-turbulent interface (TNTI) and spatial evolution of the small-scale behaviour of these different jets, which are both important factors behind determining the entrainment rate. This evolution is examined in both the streamwise direction and within the TNTI itself where the fluid adapts from a non-turbulent state, initially through the direct action of viscosity and then through nonlinear inertial processes, to the state of the turbulence within the bulk of the flow over a short distance. We show that the suppression of the coherent structures in the fractal jet leads to a less contorted interface, with large-scale excursions of the inner TNTI (that between the jet’s azimuthal shear layer and the potential core) being suppressed. Further downstream, the behaviour of the TNTI is shown to be comparable for both jets. The velocity gradients develop into a canonical state with streamwise distance, manifested as the development of the classical tear-drop shaped contours of the statistical distribution of the velocity-gradient-tensor invariants $\mathit{Q}$ and $\mathit{R}$. The velocity gradients also develop spatially through the TNTI from the irrotational boundary to the bulk flow; in particular, there is a strong small-scale anisotropy in this region. This strong inhomogeneity of the velocity gradients in the TNTI region has strong consequences for the scaling of the thickness of the TNTI in these spatially developing flows since both the Taylor and Kolmogorov length scales are directly computed from the velocity gradients.

In this study the effect of multiscale geometry on the near-field structure of an axisymmetric turbulent jet is examined at a global Reynolds number of Re G = 10, 000. With the aid of tomographic particle image velocimetry (PIV), the suppression of the coherent structures due to this fractal geometry is analysed and the changes to the near-field vorticity are evaluated. This particular geometry leads to the break-up of the azimuthal vortex rings present for round jets and to the formation of radial and streamwise opposite-signed patches of vorticity. The latter are found to be responsible for the axis-switching of the jet, a phenomenon observed for some noncircular jets where the major axis shrinks and the minor one expands in the near field, effectively switching the two axes of the jet. This was the first time, to the knowledge of the authors, that axis-switching has been observed for a jet where the coherent structures have been suppressed. Following the significant differences found in the near field, the far field is examined. There, the integral lengthscale of the large scale eddies L ur and the size of the jet evaluated in terms of the jet half-width r 1/2 are found to evolve in a similar fashion, whilst the ratio L ur /r 1/2 is found to be higher for the fractal jet than for the round jet, for which the near-field structures have not been suppressed.

Tomographic particle image velocimetry experiments were performed in the near field of the turbulent flow past a square cylinder. A classical Reynolds decomposition was performed on the resulting velocity fields into a time invariant mean flow and a fluctuating velocity field. This fluctuating velocity field was then further decomposed into coherent and residual/stochastic fluctuations. The statistical distributions of the second and third invariants of the velocity-gradient tensor were then computed at various streamwise locations, along the centreline of the flow and within the shear layers. These invariants were calculated from both the Reynolds-decomposed fluctuating velocity fields and the coherent and stochastic fluctuating velocity fields. The range of spatial locations probed incorporates regions of contrasting flow physics, including a mean recirculation region and separated shear layers, both upstream and downstream of the location of peak turbulence intensity along the centreline. These different flow physics are also reflected in the velocity gradients themselves with different topologies, as characterised by the statistical distributions of the constituent enstrophy and strain-rate invariants, for the three different fluctuating velocity fields. Despite these differing flow physics the ubiquitous self-similar 'tear drop'-shaped joint probability density function between the second and third invariants of the velocity-gradient tensor is observed along the centreline and shear layer when calculated from both the Reynolds decomposed and the stochastic velocity fluctuations. These 'tear drop'-shaped joint probability density functions are not, however, observed when calculated from the coherent velocity fluctuations. This 'tear drop' shape is classically associated with the statistical distribution of the velocity-gradient tensor invariants in fully developed turbulent flows in which there is no coherent dynamics present, and hence spectral peaks at low wavenumbers. The results presented in this manuscript, however, show that such 'tear drops' also exist in spatially developing inhomogeneous turbulent flows. This suggests that the 'tear drop' shape may not just be a universal feature of fully developed turbulence but of turbulent flows in general.

There has been much debate over the past decade or so over the scaling of the thickness of the turbulent/nonturbulent (TNT) interface for turbulent shear flows. It is generally considered to consist of the outer viscous superlayer, in which viscous processes are significant, and an inner turbulent sublayer which is dominated by inertial processes. Various authors have stated that the interface thickness scales with the Taylor length scale λ whilst others state that it scales with the Kolmogorov length scale η. Frequently, only self-similar turbulent flows are considered in which a single value of either λ or η is sufficient to scale various phenomena, including the thickness of the TNT interface. In this manuscript we show that for flows which are not self-similar the local Kolmogorov length scale increases quite significantly as you move closer to the boundary between the turbulent and non-turbulent fluid. We find that the variation of this local Kolmogorov length scale with normal distance from the TNT boundary may be collapsed by the local Kolmogorov length scale computed from the TNT boundary itself. We subsequently show that this variation in local Kolmogorov length scale occurs concurrently to an increase in the small-scale anisotropy in the TNT interface. This anisotropy peaks at the boundary between the viscous superlayer and the turbulent sublayer suggesting that these two sublayers are in fact quite distinct from one another. We show that these results hold for a number of different TNT interfaces from various flows and with the bulk turbulence being in a variety of states of development. The local viscous scaling that we obtain, along with an increase in anisotropy primarily driven by an increased magnitude of velocity gradients in the TNT-boundary-normal direction, leads us to draw an analogy between TNT interfaces and the wall in wall-bounded turbulence.