Connections between centrifugal, stratorotational, and radiative instabilities in viscous Taylor-Couette flow

Leclercq, Colin; Nguyen, Florian; Kerswell, Rich R.

doi:10.1103/physreve.94.043103

Cited by 10 publications

(25 citation statements)

References 21 publications

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“…However, the gap ratio of their set-up is smaller η = 0.8 and the Froude number is also higher F i = 0.5 than in the present experiment where F i = 0.2. Interestingly, Leclercq et al (2016) also report a high dominant azimuthal wavenumber m = 11 at instability onset when µ 0.5 for η = 0.9 and F i = 0.2.…”

Section: Experimental Observationsmentioning

confidence: 77%

“…Recently, Leclercq et al (2016) and Park et al (2017) have investigated the centrifugally unstable regime µ < η 2 by means of linear stability analyses. They both have shown that the strato-rotational instability continues to exist in this regime and is therefore in competition with the centrifugal instability.…”

Section: Introductionmentioning

confidence: 99%

“…At both ratios, they report a transition from the centrifugal instability to the strato-rotational instability at instability onset when the stratification becomes sufficiently strong. On the other hand, Leclercq et al (2016) have studied wide ranges of angular velocity ratio µ and Reynolds number for two gap ratios η = 0.417 and η = 0.9 and for three constant Froude numbers. In contrast to Park et al (2017), they argue that the two instabilities should be indistinguishable at onset because there is no discontinuity of the dominant axial wavenumber near the marginal stability curve.…”

Section: Introductionmentioning

confidence: 99%

“…The corresponding dominant azimuthal wavenumber is also always low for the gap ratio η = 0.417. However, it varies widely for η = 0.9 and this could actually indicate the presence of two different instabilities but this possibility has not been investigated by Leclercq et al (2016).…”

Section: Introductionmentioning

confidence: 99%

“…In section §4, the characteristics of the observed primary modes are compared with the predictions of the linear stability analysis. Section §5 summarizes the results and discusses them in relation to the study of Leclercq et al (2016).…”

Section: Introductionmentioning

confidence: 99%

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Competition between the centrifugal and strato-rotational instabilities in the stratified Taylor–Couette flow

et al. 2018

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The stably stratified Taylor–Couette flow is investigated experimentally and numerically through linear stability analysis. In the experiments, the stability threshold and flow regimes have been mapped over the ranges of outer and inner Reynolds numbers: $-2000<Re_{o}<2000$ and $0<Re_{i}<3000$, for the radius ratio $r_{i}/r_{o}=0.9$ and the Brunt–Väisälä frequency $N\approx 3.2~\text{rad}~\text{s}^{-1}$. The corresponding Froude numbers $F_{o}$ and $F_{i}$ are always much smaller than unity. Depending on $Re_{o}$ (or equivalently on the angular velocity ratio $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D6FA}_{o}/\unicode[STIX]{x1D6FA}_{i}$), three different regimes have been identified above instability onset: a weakly non-axisymmetric mode with low azimuthal wavenumber $m=O(1)$ is observed for $Re_{o}<0$ ($\unicode[STIX]{x1D707}<0$), a highly non-axisymmetric mode with $m\sim 12$ occurs for $Re_{o}>840$ ($\unicode[STIX]{x1D707}>0.57$) while both modes are present simultaneously in the lower and upper parts of the flow for $0\leqslant Re_{o}\leqslant 840$ ($0\leqslant \unicode[STIX]{x1D707}\leqslant 0.57$). The destabilization of these primary modes and the transition to turbulence as $Re_{i}$ increases have been also studied. The linear stability analysis proves that the weakly non-axisymmetric mode is due to the centrifugal instability while the highly non-axisymmetric mode comes from the strato-rotational instability. These two instabilities can be clearly distinguished because of their distinct dominant azimuthal wavenumber and frequency, in agreement with the recent results of Park et al. (J. Fluid Mech., vol. 822, 2017, pp. 80–108). The stability threshold and the characteristics of the primary modes observed in the experiments are in very good agreement with the numerical predictions. Moreover, we show that the centrifugal and strato-rotational instabilities are observed simultaneously for $0\leqslant Re_{o}\leqslant 840$ in the lower and upper parts of the flow, respectively, because of the variations of the local Reynolds numbers along the vertical due to the salinity gradient.

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Section: Experimental Observationsmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Competition between the centrifugal and strato-rotational instabilities in the stratified Taylor–Couette flow

et al. 2018

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On the stability of the Couette–Taylor flow between rotating porous cylinders with radial flow

Ilin

Morgulis

2020

European Journal of Mechanics - B/Fluids

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We study the stability of the Couette-Taylor flow between porous cylinders with radial throughflow. It had been shown earlier that this flow can be unstable with respect to non-axisymmetric (azimuthal or helical) waves provided that the radial Reynolds number, R (constructed using the radial velocity at the inner cylinder and its radius), is high. In this paper, we present a very detailed and, in many respects, novel chart of critical curves in a region of moderate values of R, and we show that, starting from values of R, as low as 10, the critical modes inherited from the inviscid instability gradually substitute the classical Taylor vortices. Also, we have looked more closely at the effect of a weak radial flow (relatively low R) on the Taylor instability and found that a radial flow directed from the inner cylinder to the outer one is capable of stabilizing the Couette-Taylor flow provided that the gap between the cylinders is wide enough. This observation is in a sharp contrast with the case of relatively narrow gaps for which the opposite effect is well-known.

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Layer formation and relaminarisation in plane Couette flow with spanwise stratification

2019

Self Cite

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In this paper we investigate the effect of stable stratification on plane Couette flow when gravity is oriented in the spanwise direction. When the flow is turbulent we observe near-wall layering and associated new mean flows in the form of large scale spanwiseflattened streamwise rolls. The layers exhibit the expected buoyancy scaling l z ∼ U/N where U is a typical horizontal velocity scale and N the buoyancy frequency. We associate the new coherent structures with a stratified modification of the well-known large scale secondary circulation in plane Couette flow. We find that the possibility of the transition to sustained turbulence is controlled by the relative size of this buoyancy scale to the spanwise spacing of the streaks. In parts of parameter space transition can also be initiated by a newly discovered linear instability in this system (Facchini et. al. 2018 J. Fluid Mech. vol. 853, pp. 205-234). When wall-turbulence can be sustained the linear instability opens up new routes in phase space for infinitesimal disturbances to initiate turbulence. When the buoyancy scale suppresses turbulence the linear instability leads to more ordered nonlinear states, with the possibility for intermittent bursts of secondary shear instability. † Email address for correspondence: d.lucas1@keele.ac.uk arXiv:1808.01178v3 [physics.flu-dyn]

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Connections between centrifugal, stratorotational, and radiative instabilities in viscous Taylor-Couette flow

Cited by 10 publications

References 21 publications

Competition between the centrifugal and strato-rotational instabilities in the stratified Taylor–Couette flow

Competition between the centrifugal and strato-rotational instabilities in the stratified Taylor–Couette flow

On the stability of the Couette–Taylor flow between rotating porous cylinders with radial flow

Layer formation and relaminarisation in plane Couette flow with spanwise stratification

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