Three-dimensional visualization of the interaction of a vortex ring with a stratified interface

Abstract

The study of vortex-ring-induced stratified mixing has long played a key role in understanding externally forced stratified turbulent mixing. While several studies have investigated the dynamical evolution of such a system, this study presents an experimental investigation of the mechanical evolution of these vortex rings, including the stratification-modified three-dimensional instability. The aim of this paper is to understand how vortex rings induce mixing of the density field. We begin with a discussion of the Reynolds and Richardson number dependence of the vortex-ring interaction using two-dimensional particle image velocimetry measurements. Then, through the use of modern imaging techniques, we reconstruct from an experiment the full three-dimensional time-resolved velocity field of a vortex ring interacting with a stratified interface. This work agrees with many of the previous two-dimensional experimental studies, while providing insight into the three-dimensional instabilities of the system. Observations indicate that the three-dimensional instability has a similar wavenumber to that found for the unstratified vortex-ring instability at later times. We determine that the time scale associated with this instability growth has an inverse Richardson number dependence. Thus, the time scale associated with the instability is different from the time scale of interface recovery, possibly explaining the significant drop in mixing efficiency at low Richardson numbers. The structure of the underlying instability is a simple displacement mode of the vorticity field.

The structure and origin of confined Holmboe waves

“…Using a handheld refractometer (Reichert Technologies Goldberg) it was possible to obtain the desired density difference ∆ρ while matching refractive indices within a relative error of ∆n/n ≈ 10 −4 , small enough to obtain sharp and accurate particle images. The difference in diffusivity of these solutions is negligible, and does not introduce any additional dynamics, as discussed in Olsthoorn & Dalziel (2017).…”

A comparison of entrainment in turbulent line plumes adjacent to and distant from a vertical wall

“…To determine the velocity fields, the raw particle images were processed using the 2017a PIV algorithm of Digiflow (Olsthoorn & Dalziel 2017). Interrogation windows were chosen to be with an overlap of .…”

“…For both PIV and LIF, it is necessary to eliminate refractive index variations within the fluid as these produce distortions of the light paths and lead to errors in determining the positions of the PIV particles and uncertainty in the location of the dye measurements. To obtain a negatively buoyant plume, we used sodium nitrate solutions as the plume source and sodium chloride solutions as the ambient fluid to match refractive indices while maintaining a density difference (Olsthoorn & Dalziel 2017). The refractive indices of the ambient and source fluid were matched to within but, due to entrainment, any mismatch was further reduced by the time that the plume was in the measurement region.…”

A versatile scanning method for volumetric measurements of velocity and density fields

“…A novel alternative approach was demonstrated by Olsthoorn & Dalziel (2017) where the light sheet remained at a fixed position but the experiment was effectively moved (in this case by displacing the density interface relative to the light sheet). Multiple identical experiments were conducted and stereo PIV measurements taken, with the relative light sheet position moving between each experiment.…”

“…The density difference between the reservoirs was achieved using two salt solutions, NaNO 3 and NaCl, such that the refractive indices of the solutions were matched at 532 nm (the wavelength of the laser source). This particular combination of salts was used as they, to a good approximation, mix linearly and have similar diffusivities at the low concentrations required here (Olsthoorn & Dalziel 2017). These salt solutions were added to the appropriate reservoirs to establish the desired density difference.…”