Layer formation and transitions in stratified circular Couette flow

Boubnov, B. M.; Gledzer, E. B.; Hopfinger, Emil J.; Orlandi, P.

doi:10.1016/0377-0265(95)00419-x

Cited by 13 publications

(24 citation statements)

References 5 publications

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“…Interestingly, vortex structures with a vertical size scaling like U/N have been also reported in stratified Taylor-Couette flow [23][24][25] in the strongly stratified regime. Like the previous studies, this experiment is characterized by a vertically uniform basic state.…”

Section: Introductionmentioning

confidence: 71%

“…In the strongly stratified limit, F h ϭ0, the inviscid Boussinesq equations have been shown to become self-similar with respect to the variable zN/U when no vertical lengthscales are externally imposed through boundary or initial conditions. These conditions pertain to the numerical experiments of Herring and Métais, 9 laboratory experiments of Fincham et al, 4 Billant and Chomaz, 20 Boubnov et al and Caton et al [23][24][25] This self-similarity arises because the acceleration term in the vertical momentum equation is negligible when F h Ӷ1. It implies that the vertical scale of the motion is L v ϭU/N making the scaling determinate without any further assumption.…”

Section: Discussionmentioning

confidence: 99%

“…As seen from ͑7͒-͑10͒, purely twodimensional equations for the horizontal velocity with undetermined vertical dependence are then obtained in the strongly stratified limit. In contrast, when spontaneous layering from an initially vertically uniform flow occurs as in the numerical experiments of Herring and Métais 9 or in the laboratory experiments of Fincham et al, 4 Billant and Chomaz, 20 Boubnov et al and Caton et al, [23][24][25] the layer thickness is selected dynamically by the flow itself. Because L v is not imposed by scaling arguments, the a priori assumption L v ӷU/N used by RMWL cannot be made in these cases.…”

Section: Scaling Analysismentioning

confidence: 99%

“…It is also noteworthy that the vertical velocity amplitude decreases inversely proportionally to N while density perturbations increase linearly with N. The self-similarity ͑20͒-͑22͒ explains the observations of Herring and Métais 9 in which three strongly stratified numerical experiments starting from the same initial condition but with different Brunt-Väisälä frequencies were observed to evolve identically with time. It also accounts for the results of the stratified Taylor-Couette experiments [23][24][25] and the linear stability analysis of a colum-nar vortex pair. 22 In the latter study, an increase of N for F h Ӷ1 indeed leads to a decrease of the most amplified wavelength of the zigzag instability according to ϰU/N while the maximum growth rate remains the same.…”

Section: ͑18͒mentioning

confidence: 99%

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Self-similarity of strongly stratified inviscid flows

2001

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International audienceIt is well-known that strongly stratified flows are organized into a layered pancake structure in which motions are mostly horizontal but highly variable in the vertical direction. However, what determines the vertical scale of the motion remains an open question. In this paper, we propose a scaling law for this vertical scale Lu when no vertical lengthscales are imposed by initial or boundary conditions and when the fluid is strongly stratified, i.e., when the horizontal Froude number is small: Fh=U/NLh " 1, where U is the magnitude of the horizontal velocity, N the Brunt-Vïsälä frequency and Lh the horizontal lengthscale. Specifically, we show that the vertical scale of the motion is Lv=U/N by demonstrating that the inviscid governing equations in the limit Fh?O, without any a priori assumption on the magnitude of Lu, are self-similar with respect to the variable zN/U, where z is the vertical coordinate. This self-similarity fully accounts for the layer characteristics observed in recent studies reporting spontaneous layering from an initially vertically uniform flow. For such a fine vertical scale, vertical gradients are large, O(1/FhLh). Therefore, even if the magnitude of the vertical velocity is small and scales like FhU, the leading order governing equations of these strongly stratified flows are not two-dimensional in contradiction with a previous conjecture. The self-similarity further suggests that the vertical spectrum of horizontal kinetic energy of pancake turbulence should be of the form E(kz)?N2kz-3, giving an alternative explanation for the observed vertical spectra in the atmosphere and oceans. © 2001 American Institute of Physics

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Section: Introductionmentioning

confidence: 71%

Section: Discussionmentioning

confidence: 99%

Section: Scaling Analysismentioning

confidence: 99%

Section: ͑18͒mentioning

confidence: 99%

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Self-similarity of strongly stratified inviscid flows

2001

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“…With the exception of [8], pre-2001 laboratory experiments on stratified Taylor-Couette flow were always carried out with a fixed outer cylinder [8][9][10][11][12] (so µ = 0 < η 2 ) and the relevance of the Rayleigh line was not questioned. The first experimental evidence of the SRI came in 2007 [13] where non-axisymmetric instability was clearly observed in the centrifugally-stable regime.…”

Section: Introductionmentioning

confidence: 99%

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

2016

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This is the final published version of the article (version of record). It first appeared online via APS at http://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043103. Please refer to any applicable terms of use of the publisher. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms PHYSICAL REVIEW E 94, 043103 (2016) Connections between centrifugal, stratorotational, and radiative instabilities in viscous Taylor-Couette flow The "Rayleigh line" μ = η 2 , where μ = o / i and η = r i /r o are respectively the rotation and radius ratios between inner (subscript i) and outer (subscript o) cylinders, is regarded as marking the limit of centrifugal instability (CI) in unstratified inviscid Taylor-Couette flow, for both axisymmetric and nonaxisymmetric modes. Nonaxisymmetric stratorotational instability (SRI) is known to set in for anticyclonic rotation ratios beyond that line, i.e., η 2 < μ < 1 for axially stably stratified Taylor-Couette flow, but the competition between CI and SRI in the range μ < η 2 has not yet been addressed. In this paper, we establish continuous connections between the two instabilities at finite Reynolds number Re, as previously suggested by Le Bars and Le Gal [Phys. Rev. Lett. 99, 064502 (2007)], making them indistinguishable at onset. Both instabilities are also continuously connected to the radiative instability at finite Re. These results demonstrate the complex impact viscosity has on the linear stability properties of this flow. Several other qualitative differences with inviscid theory were found, among which are the instability of a nonaxisymmetric mode localized at the outer cylinder without stratification and the instability of a mode propagating against the inner cylinder rotation with stratification. The combination of viscosity and stratification can also lead to a "collision" between (axisymmetric) Taylor vortex branches, causing the axisymmetric oscillatory state already observed in past experiments. Perhaps more surprising is the instability of a centrifugal-like helical mode beyond the Rayleigh line, caused by the joint effects of stratification and viscosity. The threshold μ = η 2 seems to remain, however, an impassable instability limit for axisymmetric modes, regardless of stratification, viscosity, and even disturbance amplitude.

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Impact of centrifugal buoyancy on strato-rotational instability

Lopez

Marqués

2020

J. Fluid Mech.

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Layer formation and transitions in stratified circular Couette flow

Cited by 13 publications

References 5 publications

Self-similarity of strongly stratified inviscid flows

Self-similarity of strongly stratified inviscid flows

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

Impact of centrifugal buoyancy on strato-rotational instability

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