Kinematics of local entrainment and detrainment in a turbulent jet

Abstract

In this paper we investigate the continuous, local exchange of fluid elements as they are entrained and detrained across the turbulent/non-turbulent interface (TNTI) in a high Reynolds number axisymmetric jet. To elucidate characteristic kinematic features of local entrainment and detrainment processes, simultaneous high-speed particle image velocimetry and planar laser-induced fluorescence measurements were undertaken. Using an interface-tracking technique, we evaluate and analyse the conditional dependence of local entrainment velocity in a frame of reference moving with the TNTI in terms of the interface geometry and the local flow field. We find that the local entrainment velocity is intermittent with a characteristic length scale of the order of the Taylor micro-scale and that the contribution to the net entrainment rate arises from the imbalance between local entrainment and detrainment rates that occurs with a ratio of two parts of entrainment to one part detrainment. On average, an increase in local entrainment is correlated with excursions of the TNTI towards jet centreline into regions of higher streamwise momentum, convex surface curvature facing the turbulent side of the jet and along the leading edges of the interface. In contrast, detrainment is correlated with excursions of the TNTI away from the jet centreline into regions of lower streamwise momentum, concave surface curvature and along the trailing edge. We find that strong entrainment is characterised by a local counterflow velocity field in the frame of reference moving with the TNTI which enhances the transport of rotational and irrotational fluid elements. On the other hand, detrainment is characterised by locally uniform flow fields with the local fluid velocity on either side of the TNTI advecting in the same direction. These local flow patterns and the strength of entrainment or detrainment rates are also observed to be strongly influenced by the presence and relative strength of vortical structures which are of the order of the Taylor micro-scale that populate the turbulent region along the jet boundary.

Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current

“…A more recent work by Mistry et al. (2019), which discusses the existence of instantaneous detrainment zones in a turbulent jet, further supports our observations on the detrainment near the VLCSs. Here, the authors show that, similarly to our findings, high detrainment is observed when the fluid moves tangentially to the interface on both sides of the TNTI.…”

“…2014; Krug et al. 2017 a ), unconditioned averages of are negative (entrainment), but instantaneous positive (detrainment) values can be observed (Mistry, Philip & Dawson 2019). To interpret the latter, one can take into account the local entrainment velocity decomposition based on the turbulent enstrophy equation introduced by Holzner & Lüthi (2011).…”

Connecting the time evolution of the turbulence interface to coherent structures

“…Hypothesizing a constant entrainment velocity over the TNTI, he concluded that, on average, the curvature/propagation effect creates TNTI area along the bulges and destroys it in the valleys of the TNTI. While this is an important theoretical finding, the local entrainment velocity is known to vary significantly along the TNTI (Holzner & Lüthi 2011;Wolf et al 2012;Watanabe et al 2014), with a predominance of negative values implying entrainment that alternate with sporadic positive values representing detrainment zones (Wolf et al 2012; Krug et al 2017a;Mistry, Philip & Dawson 2019). In this work, we evaluate locally the stretching and the curvature/propagation terms on the TNTI in order to assess their role in the time evolution of surface area of the TNTI.…”

“…Related findings were presented by Lee, Sung & Zaki (2017), who used a conditional analysis to show that the surface area of the TNTI increases in the vicinity of large-scale motions of a turbulent boundary layer. More recently, vortical structures near the TNTI have been shown to influence both the intensity of the local entrainment velocity and the mean curvature of the TNTI (Mistry et al 2019;Neamtu-Halic et al 2019). This suggests that vortical structures may impact the evolution of the TNTI area.…”

Characteristics of the turbulent non-turbulent interface in a spatially evolving turbulent mixing layer

“…da Silva & Taveira 2010;Jahanbakhshi, Vaghefi & Madnia 2015) reveal the presence of a large vorticity structure (LVS) of the order of the Taylor microscale around the TNTI. These structures are found to play an important role in the entrainment of irrotational fluid (da Mistry et al 2019). The TNTI thickness is reported to be of the order of λ owing to the presence of such LVSs around it (da Silva & Taveira 2010).…”