Axisymmetric pulse train solutions in narrow-gap spherical Couette flow

Child, Adam; Hollerbach, Rainer; Kersalé, Evy

doi:10.1016/j.physd.2017.02.009

Cited by 5 publications

(3 citation statements)

References 29 publications

(49 reference statements)

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“…Flow structures caused by the first instability are determined by the relative gap size or aspect ratio, δ = (r2 -r1)/r1, where r2 is the radius of the outer sphere. In shallow layers (for which the aspect ratio δ < 0.24) Taylor vortices [6] first appear as a result of flow instability; vortices are steady for δ > 0.02 [7]. Taylor vortices can be symmetric about the axis of rotation, as well as asymmetric about the equatorial plane [8,9].…”

mentioning

confidence: 99%

Wave number selection in the presence of noise: Experimental results

Zhilenko

Krivonosova

Gritsevich

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this study, we consider how the wave number selection in spherical Couette flow, in the transition to azimuthal waves after the first instability, occurs in the presence of noise. The outer sphere was held stationary, while the inner sphere rotational speed was increased linearly from a subcritical flow to a supercritical one. In a supercritical flow, one of two possible flow states, each with different azimuthal wave numbers, can appear depending upon the initial and final Reynolds numbers and the acceleration value. Noise perturbations were added by introducing small disturbances into the rotational speed signal. With an increasing noise amplitude, a change in the dominant wave number from m to m ± 1 was found to occur at the same initial and final Reynolds numbers and acceleration values. The flow velocity measurements were conducted by using laser Doppler anemometry. Using these results, the role of noise as well as the behaviour of the amplitudes of the competing modes in their stages of damping and growth were determined.

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mentioning

confidence: 99%

Wave number selection in the presence of noise: Experimental results

Zhilenko

Krivonosova

Gritsevich

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The instabilities in SCF are dependent on the radius ratio β and appear as a wide variety of axisymmetric and non-axisymmetric modes after the critical value of the Reynolds number is exceeded. Taylor vortices can be observed in thin rotating spherical layers at β > 0.8 [7][8][9][10], in which the centrifugal instability arises in the equatorial plane. In wide gaps with β < 0.8, more suitable for geophysical applications, the type of instability depends on whether only the inner sphere or both spheres rotate.…”

Section: Introductionmentioning

confidence: 99%

Noise induced effects in the axisymmetric spherical Couette flow

Krivonosova

Gritsevich

Zhilenko

et al. 2023

Phil. Trans. R. Soc. A.

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We study the axisymmetric, wide gap, spherical Couette flow in the presence of noise in numerical simulations and experiments. Such studies are important because most of the flows in nature are subjected to random fluctuations. Noise is introduced into the flow by adding fluctuations to the inner sphere rotation which are random in time with zero mean. Flows of a viscous incompressible fluid are induced either by rotation of the inner sphere only or by the co-rotation of the spheres. Mean flow generation was found to occur under the action of additive noise. A higher relative amplification of meridional kinetic energy compared to the azimuthal component was also observed under certain conditions. Calculated flow velocities were validated by laser Doppler anemometer measurements. A model is proposed to elucidate the rapid growth of meridional kinetic energy for flows induced by varying the co-rotation of the spheres. Our linear stability analysis for flows induced by the rotation of the inner sphere revealed a decrease in the critical Reynolds number, corresponding to the onset of the first instability. Also, in this case, a local minimum of the mean flow generation on approaching the critical Reynolds number was observed, which is consistent with the available theoretical predictions. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 2)’.

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“…The spherical Couette flow is a typical problem in the study of hydrodynamic instabilities, and is relevant to a wide range of applications in planetary atmospheres, geophysics, astrophysics, and engineering problems [1][2][3]. A lot of work has been done on the spherical Couette flow in the past, but most of them were restricted to narrow-and medium-gap clearance ratios [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. A limited number of studies were conducted for wide-gap clearance ratios [3,9,[23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow

Abbas

Shah

2018

J Braz. Soc. Mech. Sci. Eng.

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We study the existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow by time marching the three-dimensional incompressible Navier-Stokes equations numerically. Three wide-gap clearance ratios, b ¼ R 2 À R 1 ð Þ =R 1 ¼ 0:33, 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio b ¼ 0:18 at Reynolds number Re ¼ 700 as the initial conditions and suddenly increasing b to the target value, we can compute Taylor vortices for the three wide gaps. For b ¼ 0:33, Taylor vortices exist in the range 450 Re 2050. With increasing Re the steady symmetric 1-vortex flow becomes steady asymmetric at Re ¼ 1850, and then become periodic at Re ¼ 2000. When Re [ 2050 the flow returns back to the steady basic flow state with no Taylor vortices. For b ¼ 0:38, Taylor vortices can exist in the range 500 Re 1400. With increasing Re, the steady symmetric 1-vortex flow become steady asymmetric at Re ¼ 1200, and then the flow evolves into the steady basic flow for Re [ 1400. For b ¼ 0:42, Taylor vortices can exist in the range 650 Re 1300. With increasing Re, steady asymmetric Taylor vortices occur at Re ¼ 1150, and then the flow evolves into the steady basic flow for Re [ 1300. The present numerical results are in good agreement with available numerical and experimental results. Furthermore, the existence regime of Taylor vortices in the ðb; ReÞ plane for b ! 0:33 and the three-dimensional transition process from periodic asymmetric vortex flow to steady basic flow with increasing Re are presented for the first time. Keywords Spherical Couette flow Á Wide gap Á Symmetric Taylor vortices Á Asymmetric Taylor vortices

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Axisymmetric pulse train solutions in narrow-gap spherical Couette flow

Cited by 5 publications

References 29 publications

Wave number selection in the presence of noise: Experimental results

Wave number selection in the presence of noise: Experimental results

Noise induced effects in the axisymmetric spherical Couette flow

Existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow

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