The onset of convection in rotating circular cylinders with experimental boundary conditions

Zhang, Keke; Liao, Xinhao

doi:10.1017/s002211200800517x

Cited by 34 publications

(74 citation statements)

References 16 publications

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“…This traveling mode is similar to that observed in experiments in a Γ = 2 cylinder rotating at lower rotation rates (Zhong et al 1991(Zhong et al , 1993. The structure of this mode is also similar to that of the critical mode for Γ = 4, E = 5 × 10 −5 and P r = 1 computed by Zhang & Liao (2009) for which m = 10 while the asymptotic wavenumber as E → 0 is m ≈ 12. In contrast, in our case, computed for E = 10 −6 , the observed wavenumber is larger than the onset wavenumber m ≈ 4.5 in the limit E → 0.…”

Section: Nonlinear Dynamics Of Wall Modessupporting

confidence: 84%

“…We are interested in the dynamics of the wall modes which are the first unstable modes in laterally bounded rotating Rayleigh-Bénard convection. The critical Rayleigh number for the appearance of wall modes can be found in Herrmann & Busse (1993) and Kuo & Cross (1993) (see Zhang & Liao (2009) for higher order corrections) and is given in our dimensionless units by…”

Section: Nonlinear Dynamics Of Wall Modesmentioning

confidence: 99%

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Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

2019

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We show, using direct numerical simulations with experimentally realizable boundary conditions, that wall modes in Rayleigh-Bénard convection in a rapidly rotating cylinder persist even very far from their linear onset. These nonlinear wall states survive in the presence of turbulence in the bulk and are robust with respect to changes in the shape of the boundary of the container. In this sense these modes behave much like the topologically protected states present in two-dimensional chiral systems even though rotating convection is a three-dimensional nonlinear driven dissipative system. We suggest that the robustness of this nonlinear mode may provide an explanation for the strong zonal flows observed recently in simulations and experiments on rapidly rotating convection at high Rayleigh number. †

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Section: Nonlinear Dynamics Of Wall Modessupporting

confidence: 84%

Section: Nonlinear Dynamics Of Wall Modesmentioning

confidence: 99%

Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

2019

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“…The visualizations of Figure 5 have some visual resemblance to the modes for convective onset in a cylinder [37]. However, at the current parameter values these onset modes are domain-filling (and not wall-localized) with azimuthal wavenumber m = 1 and leave out the prominent jets, leading us to conclude that what we observe are not onset modes.…”

Section: Orientation-compensated Mean Flow Structure Of the Sidewamentioning

confidence: 62%

Turbulent rotating convection confined in a slender cylinder: The sidewall circulation

et al. 2020

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Recent studies of rotating Rayleigh-Bénard convection at high rotation rates and strong thermal forcing have shown a significant discrepancy in total heat transport between experiments on a confined cylindrical domain on the one hand and simulations on a laterally unconfined periodic domain on the other. This paper addresses this discrepancy using direct numerical simulations on a cylindrical domain. An analysis of the flow field reveals a region of enhanced convection near the wall, the sidewall circulation. The sidewall circulation rotates slowly within the cylinder in anticyclonic direction. It has a convoluted structure, illustrated by mean flow fields in horizontal cross-sections of the flow where instantaneous snapshots are compensated for the orientation of the sidewall circulation before averaging. Through separate analysis of the sidewall region and the inner bulk flow, we find that for higher values of the thermal forcing the heat transport in the inner part of the cylindrical domain, outside the sidewall circulation region, coincides with the heat transport on the unconfined periodic domain. Thus the sidewall circulation accounts for the differences in heat transfer between the two considered domains, while in the bulk the turbulent heat flux is the same as that of a laterally unbounded periodic domain. Therefore, experiments, with their inherent confinement, can still provide turbulence akin to the unbounded domains of simulations, and at more extreme values of the governing parameters for thermal forcing and rotation. We also provide experimental evidence for the existence of the sidewall circulation that is in close agreement with the simulation results.

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“…Though Ra s is used to indicate onset in Figure 2, the topic requires further discussion: in a finite container, instabilities often first occur as drifting waves attached to the sidewall of the container rather than as bulk motions. In the asymptotic case (E → 0), these 'wall modes' onset at [53,54]:…”

Section: Flow Regimesmentioning

confidence: 99%

A heuristic framework for next-generation models of geostrophic convective turbulence

Cheng

Aurnou

Julien

et al. 2018

Geophysical & Astrophysical Fluid Dynamics

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Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical systems, such models still inhabit modest ranges of the governing parameters that are difficult to extrapolate to planetary settings. The canonical problem of rotating Rayleigh-Bénard convection provides an alternate approach -isolating the fundamental physics in a reduced setting. Theoretical studies and asymptotically-reduced simulations in rotating convection have unveiled a variety of flow behaviors likely relevant to natural systems, but still inaccessible to direct simulation. In lieu of this, several new large-scale rotating convection devices have been designed to characterize such behaviors. It is essential to predict how this potential influx of new data will mesh with existing results. Surprisingly, a coherent framework of predictions for extreme rotating convection has not yet been elucidated. In this study, we combine asymptotic predictions, laboratory and numerical results, and experimental constraints to build a heuristic framework for cross-comparison between a broad range of rotating convection studies. We categorize the diverse field of existing predictions in the context of asymptotic flow regimes. We then consider the physical constraints that determine the points of intersection between flow behavior predictions and experimental accessibility. Applying this framework to several upcoming devices demonstrates that laboratory studies may soon be able to characterize geophysically-relevant flow regimes. These new data may transform our understanding of geophysical and astrophysical turbulence, and the conceptual framework developed herein should provide the theoretical infrastructure needed for meaningful discussion of these results. ARTICLE HISTORY

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The onset of convection in rotating circular cylinders with experimental boundary conditions

Cited by 34 publications

References 16 publications

Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

Turbulent rotating convection confined in a slender cylinder: The sidewall circulation

A heuristic framework for next-generation models of geostrophic convective turbulence

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