The intense vorticity structures near the turbulent/non-turbulent interface in a jet

Abstract

The characteristics of the intense vorticity structures (IVSs) near the turbulent/nonturbulent (T/NT) interface separating the turbulent and the irrotational flow regions are analysed using a direct numerical simulation (DNS) of a turbulent plane jet. The T/NT interface is defined by the radius of the large vorticity structures (LVSs) bordering the jet edge, while the IVSs arise only at a depth of about 5η from the T/NT interface, where η is the Kolmogorov micro-scale. Deep inside the jet shear layer the characteristics of the IVSs are similar to the IVSs found in many other flows: the mean radius, tangential velocity and circulation Reynolds number are R/η ≈ 4.6, u 0 /u ≈ 0.8, and Re Γ /Re 1/2 λ ≈ 28, where u 0 , and Re λ are the root mean square of the velocity fluctuations and the Reynolds number based on the Taylor micro-scale, respectively. Moreover, as in forced isotropic turbulence the IVSs inside the jet are well described by the Burgers vortex model, where the vortex core radius is stable due to a balance between the competing effects of axial vorticity production and viscous diffusion. Statistics conditioned on the distance from the T/NT interface are used to analyse the effect of the T/NT interface on the geometry and dynamics of the IVSs and show that the mean radius R, tangential velocity u 0 and circulation Γ of the IVSs increase as the T/NT interface is approached, while the vorticity norm |ω| stays approximately constant. Specifically R, u 0 and Γ exhibit maxima at a distance of roughly one Taylor micro-scale from the T/NT interface, before decreasing as the T/NT is approached. Analysis of the dynamics of the IVS shows that this is caused by a sharp decrease in the axial stretching rate acting on the axis of the IVSs near the jet edge. Unlike the IVSs deep inside the shear layer, there is a small predominance of vortex diffusion over stretching for the IVSs near the T/NT interface implying that the core of these structures is not stable i.e. it will tend to grow in time. Nevertheless the Burgers vortex model can still be considered to be a good representation for the IVSs near the jet edge, although it is not as accurate as for the IVSs deep inside the jet shear layer, since the observed magnitude of this imbalance is relatively small.

Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets

“…Results from DNS give R/η ≈ 5.5 in isotropic turbulence, 13 and R/η ≈ 5.3 in planar turbulent jets. 14 Figure 2(a) shows the mean VSL thickness as function of the parameter r tr using the theoretical Burgers vortex model for both R/η = 2.6 and R/η = 5.5 and several values of the parameter r tr . As can be seen the mean VSL thickness as measured The results for the model based on the Burgers vortex are represented by crosses ("+") in Fig.…”

“…The strong correlation observed for some values is however impressive because it suggests that the local VSL thickness is imposed by the eddies near the TNTI. Indeed the TNTI is (partially) defined by the outer boundary of the IVS, 14 and therefore in this case the distance from the VSL to the maximum local vorticity magnitude l Notice that this explanation is not inconsistent with the absence of correlation between δ ν and max(ω) displayed in Figure 3(b) because in a Burgers vortex the maximum vorticity is ω 0 = /2π where is the vortex circulation and is independent from the size of the vortex core radius R BV . Finally, the lack of correlation observed for the more intense values of δ ν and l max ω (e.g., for δ ν /η > 13) in Figure 3(c) can be explained by the contribution of the "incoherent" vorticity in defining the TNTI.…”

Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers

“…Since the left-hand side of Eqs. (10), (18) and (27) should also be the same (neglecting fluctuations in the definitions of δ), it follows that the averaged…”

Lagrangian properties of the entrainment across turbulent/non-turbulent interface layers

“…19 Indeed, eddies with core radius of about 5η (≈δ ν ) were observed within the TSL. 20 Figure 3(a) shows the pdf of the cosine of the angle between δx and n, which has a large peak associated with a parallel alignment of these vectors. Thus, for small τ the particles are located in the irrotational boundary normal direction as expected from Eq.…”