Vortex-ring-induced stratified mixing

Olsthoorn, Jason; Dalziel, Stuart B.

doi:10.1017/jfm.2015.492

Cited by 18 publications

(19 citation statements)

References 23 publications

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“…The vortex tube was inserted to an approximate depth of 0.13m. This setup is similar to that found in Olsthoorn & Dalziel (2015). In both the vertical-slice measurements found here and the horizontal-slice measurements found below, the base of the vortex tube was always positioned at least two vortex diameters away from the density interface.…”

Section: Vertical-slice Observationssupporting

confidence: 82%

“…The stratification was generated using a peristaltic pump to slowly inject the denser fluid (ρ 2 ) beneath a layer of less dense fluid (ρ 1 ). This methodology has been previously shown to produce sharp interfaces (Olsthoorn & Dalziel 2015). Typically, these two fluid layers would have different refractive indexes, which distort the camera images.…”

Section: Vertical-slice Observationsmentioning

confidence: 99%

“…This paper presents an experimental investigation of the stability of vortex rings in a stratified environment. Understanding the mechanics of this interaction will help quantify why vortex rings have been observed to be such efficient mixers (Olsthoorn & Dalziel 2015). We begin with an analysis of the two-dimensional dynamics of the vortex rings as they impact a density interface.…”

Section: Introductionmentioning

confidence: 99%

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

Olsthoorn

Dalziel

2017

J. Fluid Mech.

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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.

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Section: Vertical-slice Observationssupporting

confidence: 82%

Section: Vertical-slice Observationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Olsthoorn

Dalziel

2017

J. Fluid Mech.

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“…At the other end of the spectrum, strong stratification leads to an entrainment velocity u e /u ∝ Ri −1 b in the experiments by Kato and Philipps (1969). Hence a constant mixing efficiency follows, as has been confirmed by several more recent strongly stratified turbulence experiments (see Olsthoorn and Dalziel (2015) and references therein). In the research work of Shih et al (2005) a constant mixing coefficient Γ ≈ 0.2 was found for buoyancy Reynolds numbers in the range 7 < Re b < 100 in a series of DNS of stratified sheared turbulence but the mixing coefficient then varied as Γ ∝ Re In summary, the parameters that seem to affect mixing in stratified turbulence are the Froude number and the buoyancy Reynolds number.…”

Section: Introductionsupporting

confidence: 74%

Mixing efficiency in stratified turbulence

2016

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We consider mixing of the density field in stratified turbulence and argue that, at sufficiently high Reynolds numbers, stationary turbulence will have a mixing efficiency and closely related mixing coefficient described solely by the turbulent Froude number$Fr={\it\epsilon}_{k}/(Nu^{2})$, where${\it\epsilon}_{k}$is the kinetic energy dissipation,$u$is a turbulent horizontal velocity scale and$N$is the Brunt–Väisälä frequency. For$Fr\gg 1$, in the limit of weakly stratified turbulence, we show through a simple scaling analysis that the mixing coefficient scales as${\it\Gamma}\propto Fr^{-2}$, where${\it\Gamma}={\it\epsilon}_{p}/{\it\epsilon}_{k}$and${\it\epsilon}_{p}$is the potential energy dissipation. In the opposite limit of strongly stratified turbulence with$Fr\ll 1$, we argue that${\it\Gamma}$should reach a constant value of order unity. We carry out direct numerical simulations of forced stratified turbulence across a range of$Fr$and confirm that at high$Fr$,${\it\Gamma}\propto Fr^{-2}$, while at low$Fr$it approaches a constant value close to${\it\Gamma}=0.33$. The parametrization of${\it\Gamma}$based on$Re_{b}$due to Shihet al.(J. Fluid Mech., vol. 525, 2005, pp. 193–214) can be reinterpreted in this light because the observed variation of${\it\Gamma}$in their study as well as in datasets from recent oceanic and atmospheric measurements occurs at a Froude number of order unity, close to the transition value$Fr=0.3$found in our simulations.

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“…In a recent study, Olsthoorn and Dalziel had compared the mixing efficiency of a sharp interface, perturbed by periodic vortex pairs [10,11]. They found that under certain flow conditions, mixing efficiency was independent of Richardson number.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal disruption of thermocline by successive laminar vortex pairs in a single tank thermal energy storage

Tinaikar

Advaith

Chetia

et al. 2016

Applied Thermal Engineering

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The stratification efficiency of single tank thermal energy storage is affected by the internal mixing processes, especially in the thermocline region due to disturbances of different kinds. To study the mixing dynamics at the interface, we have conducted detailed numerical and supporting experimental studies for different Atwood numbers (stratification levels). Numerical experiments were conducted with two successive vortex pairs with three different time-lags (short, medium and long). For the short time-lag case, the preliminary vortex pair merges with the ensuing vortex pair. The merged single vortex pair peels back the thermocline layer causing mixing of the hot and cold fluids. The thermocline thickness increases as a result of the entrainment of the cold fluid into the hot fluid. The peeling process continues until buoyant forces leads to plume like structures that penetrate into the lighter fluid. For the medium and large time-lag cases, such merging of vortices was not observed. The vortex pair interacts separately with the thermocline region. The plume structure created by the first vortex pair interacts with the ensuing vortex pair. The altered interface (thermocline) thickness strongly depends on the nature of the vortex-thermocline interaction mechanisms. The thermocline effectiveness decreases consequent to such interactions and have been quantified in details in the current work.

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Vortex-ring-induced stratified mixing

Cited by 18 publications

References 23 publications

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

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

Mixing efficiency in stratified turbulence

Spatio-temporal disruption of thermocline by successive laminar vortex pairs in a single tank thermal energy storage

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