Interaction of vortex ring with a stratified finite thickness interface

Abstract

This work experimentally investigates the dynamics of interaction between a propagating vortex ring and density stratified interface of finite thickness. The flow evolution has been quantified using a high speed shadowgraph technique and particle image velocimetry. The spatial and temporal behaviours of the vortex in the near and far field of the interface and the plume structure formed due to buoyancy are investigated systematically by varying the vortex strength (Reynolds number, Re) and the degree of stratification (Atwood number, At). Maximum penetration length (Lpmax) of the vortex ring through the interface is measured over a range of Reynolds (1350 ≤ Re ≤ 4600) and Richardson (0.1 ≤ Ri ≤ 4) numbers. It is found that for low Froude number values, the maximum penetration length varies linearly with the Froude number as in the study of Orlandi et al. [“Vortex rings descending in a stratified fluid,” Phys. Fluids 10, 2819–2827 (1998)]. However, for high Reynolds and Richardson numbers (Ri), anomalous behaviour in maximum penetration is observed. The Lpmax value is used to characterize the vortex-interface interactions into non-penetrative, partially-penetrative, and extensively penetrative regimes. Flow visualization revealed the occurrence of short-wavelength instability of a plume structure, particularly in a partially penetrative regime. Fluid motion exhibits chaotic behaviour in an extensively penetrative regime. Detailed analyses of plume structure propagation are performed by measuring the plume length and plume rise. Appropriate scaling for the plume length and plume rise is derived, which allows universal collapse of the data for different flow conditions. Some information concerning the instability of the plume structure and decay of the vortex ring is obtained using proper orthogonal decomposition.

Dynamics of the interaction of synthetic jet vortex rings with a stratified interface

“…These vortices are generated by baroclinic torque associated with variations in vertical pressure and horizontal density gradients caused by the vortex impinging on the density interface, as suggested by Advaith et al. (2017). With radial stretching of the PV2, the SV2 in water continues to orbit the PV2 as described above, while the SV2 in oil gradually decays (figure 5 f 1, f 2).…”

“…According to vorticity-transportation equation in a variable density flow (Advaith et al. 2017): the last term depicts baroclinic torque and can be written as in a two-dimensional case, thus leading to the generation of opposite sign vorticity to that of the primary vortex ring. As a result, the vorticity cancellation occurs along the edge of the induced boundary layer due to the interaction between the primary vortex ring and baroclinic vorticity, and that is believed to be the major cause for the circulation reduction of the primary vortex ring during the vortex–interface interaction (Chu et al.…”

“…However, for many practical situations, the formation and evolution of the vortex exist in a non-uniform or stratified environment, such as the wake of aircrafts and vessels in the stratified flow, convection of thermals in the inversion layer, interaction of flame fronts with the turbulent flow, diffusion of contaminants in the atmosphere and halocline in oceans (Dahm, Scheil & Tryggvason 1989; Sarpkaya 1996; Advaith et al. 2017). As a result, the dynamics of the vortex ring can be more complex under the influence of the interaction with the stratified interface.…”

“…In a similar stratified environment, Advaith et al. (2017) studied the vortex behaviour by particle image velocimetry (PIV) over a range of Re = 1350–4600 and Ri = 0.1–4. The scenarios of the vortex–interface interaction were characterized into non-penetrative, partially penetrative and extensively penetrative regimes.…”

“…Over the past few decades, the dynamics of the vortex ring evolving in a uniform environment has been well established in theory (Shusser & Gharib 2000;Krueger 2005;Sullivan et al 2008), experiment (Maxworthy 1977;Glezer 1988;Cater, Soria & Lim 2004;Das, Bansal & Manghnani 2017) and numerical simulation (Shariff, Verzicco & Orlandi 1994;Archer, Thomas & Coleman 2008;Lin et al 2020). However, for many practical situations, the formation and evolution of the vortex exist in a non-uniform or stratified environment, such as the wake of aircrafts and vessels in the stratified flow, convection of thermals in the inversion layer, interaction of flame fronts with the turbulent flow, diffusion of contaminants in the atmosphere and halocline in oceans (Dahm, Scheil & Tryggvason 1989;Sarpkaya 1996;Advaith et al 2017). As a result, the dynamics of the vortex ring can be more complex under the influence of the interaction with the stratified interface.…”