Importance of small-scale anisotropy in the turbulent/nonturbulent interface region of turbulent free shear flows

Abstract

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.

Turbulent entrainment into a cylinder wake from a turbulent background

“…The no-grid case, as described by run 1a, produces results that are similar to those of Buxton et al. (2019), with an increase in anisotropy being observed near the wake boundary on the wake side of the interface. A very gradual increase in the anisotropy ratio is also observed on the free-stream side of the wake boundary, however, the magnitude of this increase in not comparable to the behaviour inside the wake.…”

“…Figures 9(a) and 9(b) depict the behaviour of Σ for runs that belong to groups 1 and 2 and group 3, respectively. The no-grid case, as described by run 1a, produces results that are similar to those of Buxton et al (2019), with an increase in anisotropy being observed near the wake boundary on the wake side of the interface. A very gradual increase in the anisotropy ratio FIGURE 9.…”

“…In a study examining the turbulent/non-turbulent interface, Buxton, Breda & Dhall (2019) showed an increase in small-scale anisotropy in the interface region. They examined the behaviour of the anisotropy ratio, , as defined by, on the turbulent side of the boundary.…”

Numerical experiments on turbulent entrainment and mixing of scalars

“…The intensityυ int is produced by an anisotropic field of motion characterized by large-scale engulfment events while the intensity υ int is produced by essentially isotropic small-scale fluctuations. It is then possible to argue that only the anisotropic part of the velocity field significantly contributes to the net propagation of scalars in agreement with a number of recent works (Cimarelli et al 2015(Cimarelli et al , 2021Buxton, Breda & Dhall 2019). Accordingly, we introduce the isotropy indicator…”

Behaviour of small-scale turbulence in the turbulent/non-turbulent interface region of developing turbulent jets

“…This led to a spatial resolution (worst case) for the TPIV experiment of 11η at x/D e = 2, of 9η at x/D e = 10 and of 5η at x/D e = 25. These worst case figures are quoted assuming a Kolmogorov length scale computed from the bulk of the turbulent flow, although since the dissipation rate is known to reduce as the irrotational boundary is approached (van Reeuwijk & Holzner 2014;Buxton et al 2019) the "local" Kolmogorov length scale is around 20-25% larger hence the spatial resolution is accordingly finer than these worst-case scenarios. In terms of the longitudinal Taylor lengthscale, the spatial resolution ranged between 0.3λ f and 0.1λ f at the three locations studied.…”