Simulation of spiral instabilities in wide-gap spherical Couette flow

Abbas, Suhail; Li, Yuan; Shah, Abdullah

doi:10.1088/1873-7005/aa9d77

Cited by 17 publications

(13 citation statements)

References 33 publications

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“…It was confirmed that some of these values align remarkably well with theoretical predictions based on linear stability analysis [12][13][14]. A recent investigation with a further increase in the Reynolds number suggested relaminarization, non-uniqueness, and hysteresis in successive transition processes in an SCF [15][16][17][18]. These aspects in a wide-gap SCF can be regarded as a type of competition among different polygonal structures, which plays an important role in the route to turbulence.…”

Section: Introductionsupporting

confidence: 77%

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Bifurcation aspect of wide-gap spherical Couette flow emphasizing polygonal coherence and wave numbers observed over transitional Reynolds numbers

Goto,

Itano,

Sugihara-Seki

et al. 2021

Preprint

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This study numerically investigates the bifurcation aspect of the wide-gap spherical Couette flow (SCF), with an emphasis on the competition among polygonal coherence with different wave numbers observed over transitional Reynolds numbers. Focusing on a representative case, the half-radius ratio η = 1/2, we confirm that the axisymmetric state becomes unstable over the first transitional Reynolds number at which the 4-fold spiral state bifurcates, using the continuation method based on the Newton-Raphson algorithm. The Galerkin-spectral method was employed to numerically solve the governing equations. It is found that the 3-fold spiral state bifurcates from the axisymmetric state at a slightly higher Reynolds number than the first transitional Reynolds number. The attraction of the 3-fold spiral state expands rapidly with an increase in the Reynolds number, which is determined by verifying the distance of the unstable periodic-like state to both spiral states in the state space. This aspect of the state space explains the experimentally bistable realization of different equilibrium states over the first transitional Reynolds number. This study also found that the periodic-like state is composed of the 3-and 4-fold spiral states, similar to a beat with two different frequencies.

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Section: Introductionsupporting

confidence: 77%

“…[9] at η = 1/2 and Ref. [15,18] at η = 2/3), and they are located at the values (η, Ra) where the state was obtained experimentally or numerically. cases and found that the transition was initiated by the axisymmetric Taylor vortices with successive instability where η > 3/4, as observed in the cylindrical Taylor-Couette flow [15].…”

Section: Resultsmentioning

confidence: 87%

Bifurcation aspect of wide-gap spherical Couette flow emphasizing polygonal coherence and wave numbers observed over transitional Reynolds numbers

Goto,

Itano,

Sugihara-Seki

et al. 2021

Preprint

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show abstract

“…This is associated with the non-uniqueness of the equilibrium states realisable via hysteresis over Re cr , as reported in Ref. [5], which have been investigated in detail numerically [25]. Hereafter, we refer to the non-axisymmetric equilibrium state with m spiral arms from a pole as an "m-fold spiral state".…”

Section: Resultsmentioning

confidence: 75%

Numerical study on the axisymmetric state in spherical Couette flow under unstable thermal stratification

2019

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This paper numerically investigates the shear flow between double concentric spherical boundaries rotating differentially, so-called spherical Couette flow, under unstable thermal stratification, focusing on the boundary of the axisymmetric/non-axisymmetric transition in wide gap cases where the inner radius is comparable to the clearance width. While the transition of SCF has been confirmed experimentally in cases without thermal factor, insufficient knowledge on SCF subject to thermal instability, related to geophysical problems especially in wide gap cases, has been accumulated mainly based on numerical analysis; our motivation is to bridge the knowledge gap by a parameter extension. We reconfirm that the transition under no thermal effect is initiated by a disturbance visualised as a spiral pattern with n arms extending from the equatorial zone to the pole in each hemisphere, at the critical Reynolds number, Re cr , as previously reported. With increasing thermal factor, the buoyancy effect assists the system rotation to trigger a transition towards non-axisymmetric states, resulting in a relative decrease of Re cr . This is in contrast with the result that the system rotation apparently suppresses via Coriolis effect the transition to the thermally convective states at low Reynolds numbers. The present study elucidates that the existence of the axisymmetric state is restricted within a closed area in the extended parameter space, along the boundary of which the spiral patterns observed experimentally in SCF continually connect to the classical spherical Bénard convective states.

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“…At a certain critical Re c nonaxisymmetric instabilities give rise to regular flows whose pattern and topology depend strongly on the gap width χ = r i /r o (with r i and r o being the inner and outer radii) of the problem. When the shell is thin, Taylor-Görtler vortices develop [20][21][22] contrasting with the spiral waves [23][24][25] preferred at wider gaps. In the latter case, triadic resonances were found in a recent study (see Ref.…”

Section: Introductionmentioning

confidence: 99%

Chaotic wave dynamics in weakly magnetized spherical Couette flows

García

Seilmayer

Giesecke

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Direct numerical simulations of a liquid metal filling the gap between two concentric spheres are presented. The flow is governed by the interplay between the rotation of the inner sphere (measured by the Reynolds number Re) and a weak externally applied axial magnetic field (measured by the Hartmann number Ha). By varying the latter a rich variety of flow features, both in terms of spatial symmetry and temporal dependence, is obtained. Flows with two or three independent frequencies describing their time evolution are found as a result of Hopf bifurcations. They are stable on a sufficiently large interval of Hartmann numbers where regions of multistability of two, three and even four types of these different flows are detected. The temporal character of the solutions is analysed by means of an accurate frequency analysis and Poincaré sections. An unstable branch of flows undergoing a period doubling cascade and frequency locking of three-frequency solutions is described as well. a)

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Simulation of spiral instabilities in wide-gap spherical Couette flow

Cited by 17 publications

References 33 publications

Bifurcation aspect of wide-gap spherical Couette flow emphasizing polygonal coherence and wave numbers observed over transitional Reynolds numbers

Bifurcation aspect of wide-gap spherical Couette flow emphasizing polygonal coherence and wave numbers observed over transitional Reynolds numbers

Numerical study on the axisymmetric state in spherical Couette flow under unstable thermal stratification

Chaotic wave dynamics in weakly magnetized spherical Couette flows

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