Global stability of spiral flow

Joseph, Daniel D.; Munson, B. R.

doi:10.1017/s0022112070002574

Cited by 29 publications

(16 citation statements)

References 21 publications

(22 reference statements)

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“…The agreement is quite good in all cases; the detailed comparisons are available in Takeuchi (1979). A second verification is provided by a theoretical result due to Joseph & Munson (1970). They have shown, in the present notation, that Independent calculations of both sides of (13) showed agreement to the accuracy of the computer.…”

Section: Solution Methodssupporting

confidence: 56%

A numerical and experimental investigation of the stability of spiral Poiseuille flow

1981

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The linear stability of the spiral motion induced between concentric cylinders by an axial pressure gradient and independent cylinder rotation is studied numerically and experimentally for a wide-gap geometry. A three-dimensional disturbance is considered. Linear stability limits in the form of Taylor numbers TaL are computed for the rotation ratios μ, = 0, 0·2, and -0·5 and for values of the axial Reynolds number Re up to 100. Depending on the values of μ and Re, the disturbance which corresponds to TaL can have a toroidal vortex structure or a spiral form. Aluminium-flake flow visualization is used to determine conditions for the onset of a secondary motion and its structure at finite amplitude. The experimental results agree with the predicted values of TaL for μ [ges ] 0, and low Reynolds number. For other cases in which agreement is only fair, apparatus length is shown to be a contributing influence. The comparison between experimental and predicted wave forms shows good agreement in overall trends.

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Section: Solution Methodssupporting

confidence: 56%

A numerical and experimental investigation of the stability of spiral Poiseuille flow

1981

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“…where the implication is that all streamwise disturbances decay for Re < Re E regardless of their amplitude. The latter maximisation corresponds to 1/Re E for an unstratified, non-rotating layer where Re E = 1 2 √ 1708 ≈ 20.7 [25] under non-slip conditions. The minimisation problem has the minimum 2 2Ω(1 − 2Ω) for 0 ≤ Ω ≤ 1 2 and 0 otherwise for real λ.…”

Section: Discussionmentioning

confidence: 94%

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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“…A third issue is finite‐amplitude or non‐linear hydrodynamical instability in Rayleigh‐stable regimes. Few theoretical studies on this subject exist (Serrin 1959; Joseph & Munson 1970). It has been argued from experiments that a rapid Couette flow can be non‐linearly unstable (Richard & Zahn 1999).…”

Section: Discussionmentioning

confidence: 99%

Magnetorotational instability in a rotating liquid metal annulus

Goodman

Kageyama

2001

Monthly Notices of the Royal Astronomical Society

170

154

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Although the magnetorotational instability (MRI) has been widely accepted as a powerful accretion mechanism in magnetized accretion discs, it has not been realized in the laboratory. The possibility of studying MRI in a rotating liquid metal annulus (Couette flow) is explored by local and global stability analysis. Stability diagrams are drawn in dimensionless parameters, and also in terms of the angular velocities at the inner and outer cylinders. It is shown that MRI can be triggered in a moderately rapidly rotating table‐top apparatus, using easy‐to‐handle metals such as gallium. Practical issues of this proposed experiment are discussed.

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Global stability of spiral flow

Cited by 29 publications

References 21 publications

A numerical and experimental investigation of the stability of spiral Poiseuille flow

A numerical and experimental investigation of the stability of spiral Poiseuille flow

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

Magnetorotational instability in a rotating liquid metal annulus

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