Non-invasive turbulent mixing across a density interface in a turbulent Taylor–Couette flow

Woods, Andrew W.; Caulfield, C. P.; Landel, Julien R.; Kuesters, A.

doi:10.1017/s0022112010004295

Cited by 22 publications

(21 citation statements)

References 25 publications

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“…Nevertheless, the approach has still provided detailed insight into the sustaining mechanisms and mixing processes at work in these flows. In particular we have established that mixing can occur from two distinct mechanisms; overturning and scouring, consistently with the classification presented by Woods et al (2010). Scouring is observed when stratification is strong and overturns when the stratification is weak enough to allow small gradient Richardson numbers.…”

Section: Discussionsupporting

confidence: 86%

Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence

Lucas

Caulfield

2017

J. Fluid Mech.

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We consider turbulence driven by a large-scale horizontal shear in Kolmogorov flow (i.e. with sinusoidal body forcing) and a background linear stable stratification with buoyancy frequency N 2 B imposed in the third, vertical direction in a fluid with kinematic viscosity ν. This flow is known to be organised into layers by nonlinear unstable steady states, which incline the background shear in the vertical and can be demonstrated to be the finite-amplitude saturation of a sequence of instabilities, originally from the laminar state. Here, we investigate the next order of motions in this system, i.e. the timedependent mechanisms by which the density field is irreversibly mixed. This investigation is achieved using 'recurrent flow analysis'. We identify (unstable) periodic orbits, which are embedded in the turbulent attractor, and use these orbits as proxies for the chaotic flow. We find that the time average of an appropriate measure of the 'mixing efficiency' of the flow E = χ/(χ + D) (D is the volume-averaged kinetic energy dissipation rate and χ is the volume-averaged density variance dissipation rate) varies non-monotonically with the time-averaged buoyancy Reynolds numbers Re B = D/(νN 2 B ), and is bounded above by 1/6, consistently with the classical model of Osborn (1980). There are qualitatively different physical properties between the unstable orbits that have lower irreversible mixing efficiency at low Re B ∼ O(1) and those with nearly optimal E 1/6 at intermediate Re B ∼ 10. The weaker orbits, inevitably embedded in more strongly stratified flow, are characterised by straining or 'scouring' motions, while the more efficient orbits have clear overturning dynamics in more weakly stratified, and apparently shear-unstable flow.

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Section: Discussionsupporting

confidence: 86%

Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence

Lucas

Caulfield

2017

J. Fluid Mech.

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“…an annular stratified flow driven by rotation of the inner cylindrical boundary (see Woods et al (2010); Oglethorpe, Caulfield & Woods (2013)) suggest strongly that non-diffusive 'scouring' entrainment processes do occur, supporting a large body of previous experimental work, dating back at least to Turner (1968) and Kato & Phillips (1969). Quite recently, Oglethorpe, Caulfield & Woods (2013) established in stratified Taylor-Couette flow that the mixing does indeed vary non-monotonically with stratification, and that layers do indeed spontaneously form in an initially linearly stratified fluid.…”

Section: Introductionsupporting

confidence: 62%

Entrainment and mixed layer dynamics of a surface-stress-driven stratified fluid

Manucharyan

Caulfield

2015

J. Fluid Mech.

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We consider experimentally a linearly stratified fluid with buoyancy frequency N in a cylinder subject to surface-stress forcing from a disc of radius R spinning at a constant angular velocity Ω. We observe the growth of the disc-adjacent turbulent mixed layer bounded by a sharp primary interface with a constant thickness l I . To a good approximation the depth of the mixed layer scales as h U /R ∼ (N/Ω) −2/3 (Ωt) 2/9 . Generalising the previous arguments and observations of Shravat, Cenedese & Caulfield (2012), we show that such a deepening rate is consistent with three central assumptions that allow us to develop a phenomenological energy balance model for the entrainment dynamics. First, the total kinetic energy of the deepening mixed layer K U ∝ h U u 2 U , where u U is a characteristic velocity scale of the turbulent motions within the upper layer, is essentially independent of time and the buoyancy frequency N . Second, the scaled entrainment parameter E =ḣ U /u U , depends only on the local interfacial Richardson number. Third, the potential energy production is driven by the local energy input at the interface, and hence is proportional to the third power of this characteristic velocity u U . We establish that internal consistency between these assumptions implies that the rate of increase of the potential energy decreases with Ri I , suggesting following Phillips (1972), that the mixing in the vicinity of the primary interface leads to the spontaneous appearance of secondary partially-mixed layers which we indeed observe experimentally below the primary interface.

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“…Although we refer to this behavior as 'generic', it is important to note that the existence of the early L T L O regime, particularly associated with relatively large-scale overturnings, is not guaranteed in the evolution of all shear-unstable flows, and is likely to be environment-dependent. For example, Kelvin-Helmholtz billows in an energetic estuary have been shown not to evolve distinct vorticity cores which store potential energy with the effective L T being relatively small (Geyer et al 2010) while other forms of shear instability (such as the Holmboe instability, see Salehipour et al (2016a) for further details) are not characterized by large overturns, but rather drive mixing principally through 'scouring' (Woods et al 2010).…”

Section: Discussionmentioning

confidence: 99%

Role of overturns in optimal mixing in stratified mixing layers

2017

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Turbulent mixing plays a major role in enabling the large-scale ocean circulation. The accuracy of mixing rates estimated from observations depends on our understanding of basic fluid mechanical processes underlying the nature of turbulence in a stratified fluid. Several of the key assumptions made in conventional mixing parameterizations have been increasingly scrutinized in recent years, primarily on the basis of adequately high resolution numerical simulations. We add to this evidence by compiling results from a suite of numerical simulations of the turbulence generated through stratified shear instability processes. We study the inherently intermittent and time-dependent nature of wave-induced turbulent life cycles and more specifically the tight coupling between inherently anisotropic scales upon which small-scale isotropic turbulence grows. The anisotropic scales stir and stretch fluid filaments enhancing irreversible diffusive mixing at smaller scales. We show that the characteristics of turbulent mixing depend on the relative time evolution of the Ozmidov length scale $L_{O}$ compared to the so-called Thorpe overturning scale $L_{T}$ which represents the scale containing available potential energy upon which turbulence feeds and grows. We find that when $L_{T}\sim L_{O}$, the mixing is most active and efficient since stirring by the largest overturns becomes ‘optimal’ in the sense that it is not suppressed by ambient stratification. We argue that the high mixing efficiency associated with this phase, along with observations of $L_{O}/L_{T}\sim 1$ in oceanic turbulent patches, together point to the potential for systematically underestimating mixing in the ocean if the role of overturns is neglected. This neglect, arising through the assumption of a clear separation of scales between the background mean flow and small-scale quasi-isotropic turbulence, leads to the exclusion of an highly efficient mixing phase from conventional parameterizations of the vertical transport of density. Such an exclusion may well be significant if the mechanism of shear-induced turbulence is assumed to be representative of at least some turbulent events in the ocean. While our results are based upon simulations of shear instability, we show that they are potentially more generic by making direct comparisons with $L_{T}-L_{O}$ data from ocean and lake observations which represent a much wider range of turbulence-inducing physical processes.

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Non-invasive turbulent mixing across a density interface in a turbulent Taylor–Couette flow

Cited by 22 publications

References 25 publications

Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence

Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence

Entrainment and mixed layer dynamics of a surface-stress-driven stratified fluid

Role of overturns in optimal mixing in stratified mixing layers

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