Non-axisymmetric instabilities in basic state spherical Couette flow

Hollerbach, Rainer; Junk, Markus; Egbers, Christoph

doi:10.1016/j.fluiddyn.2006.01.001

Cited by 62 publications

(84 citation statements)

References 12 publications

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“…They can be explained by a continuously decreasing β due to a decreasing fluid depth towards the outer boundary. Such spiral-shaped waves have also been found experimentally by Egbers & Rath (1995) and numerically by Hollerbach, Junk & Egbers (2006) considering only inner sphere rotation. The spherical geometry with flat differentially rotating disks leads to a discontinuity in β.…”

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confidence: 59%

Experimental survey of linear and nonlinear inertial waves and wave instabilities in a spherical shell

2016

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We experimentally study linear and nonlinear inertial waves in a spherical shell with a radius ratio of η = 1/3. The shell rotates with a mean angular velocity Ω 0 around its vertical axis. This rotation is overlaid by a time-periodic libration of the inner sphere in the range 0 < ω lib < 2Ω 0 to excite inertial waves with a defined frequency. In the first part, we investigate linear inertial waves. The influence of the libration amplitude and the libration frequency on the waves and further the efficiency of the forcing to excite linear inertial waves will be discussed. For this, qualitative data from Kalliroscope visualisation in a meridional laser plane, as well as quantitative particle image velocimetry (PIV) data in a horizontal plane, have been analysed. A simple two-dimensional ray-tracing model is applied for the meridional plane to interpret the visualisations with respect to energy focusing and wave attractors. For sufficiently high/low libration amplitudes/frequencies, the Stewartson layer, a vertical shear layer tangential to the inner sphere's equator, becomes unstable. This so-called 'supercritical' regime, where centrifugal and shear instabilities occur, allows for nonlinear wave coupling. PIV analyses in the horizontal laser plane in the corotating frame show low-frequency structures that correspond to Rossby-wave instabilities of the Stewartson layer. Some of these are travelling retrograde and are trapped near the Stewartson layer, others are travelling prograde filling the whole gap outside the Stewartson layer. Since libration can be viewed as a time-periodic variation of differential rotation, we assume that these two different structures are related to either the retrograde (Ro d < 0) or the prograde (Ro d > 0) phase of the libration cycle. The experimental results confirm theoretical, numerical as well as other experimental studies on Stewartson-layer instabilities.

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confidence: 59%

Experimental survey of linear and nonlinear inertial waves and wave instabilities in a spherical shell

2016

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“…There are two reasons for reconsidering this problem. First, Hollerbach et al (2006), hereafter referred to as paper II, considered non-axisymmetric instabilities in non-magnetic spherical Couette flow, and obtained results completely different from the strongly magnetic results in I. It is therefore of interest to map out the transition from one regime to the other, and indeed we will find some quite unexpected behaviour in the intermediate regime.…”

Section: Introductionmentioning

confidence: 93%

Non-axisymmetric instabilities in magnetic spherical Couette flow

Hollerbach

2009

Proc. R. Soc. A.

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103

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We investigate numerically the flow of an electrically conducting fluid confined in a spherical shell, with the outer sphere stationary, the inner sphere rotating and a magnetic field imposed parallel to the rotation axis. We compute both the axisymmetric basic states and their non-axisymmetric instabilities. Two distinct instability classes emerge, one connected to previous non-magnetic results, the other to previous strongly magnetic results. Both instabilities arise from the basic state's meridional circulation, but are otherwise very different from one another, and are separated by a region of stability that persists even for large Reynolds numbers. Finally, we compute the fully three-dimensional nonlinear equilibration of both instabilities. The second class exhibits a rich variety of secondary bifurcations, involving mode transitions between different azimuthal wave numbers.

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“…Indeed, it is well known that for sufficiently large Reynolds number, the equatorial jet becomes unstable to non-axisymmetric perturbations, and gives rise to a Kelvin-Helmoltz instability [25], [26], [27]. The critical wavenumber for this instability depends on the aspect ratio and on the Reynolds number.…”

Section: Comparison With Experiments: Axial Field and Outer Spherementioning

confidence: 99%

Instabilities in magnetized spherical Couette flow

Gissinger

Goodman

2011

Phys. Rev. E

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We report 3D numerical simulations of the flow of an electrically conducting fluid in a spherical shell when an magnetic field is applied. Different spherical Couette configurations are investigated, by varying the rotation ratio between the inner and the outer sphere, the geometry of the imposed field, and the magnetic boundary conditions on the inner sphere. Either a Stewartson layer or a Shercliff layer, accompanied by a radial jet, can be generated depending on the rotation speeds and the magnetic field strength, and various non-axisymmetric destabilizations of the flow are observed. We show that instabilities arising from the presence of boundaries present striking similarities with the magnetorotational instability (MRI). To this end, we compare our numerical results to experimental observations of the Maryland experiment [Sisan et al, Phys. Rev. Lett. 93, 114502 (2004)], who claimed to observe MRI in a similar setup.

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Non-axisymmetric instabilities in basic state spherical Couette flow

Cited by 62 publications

References 12 publications

Experimental survey of linear and nonlinear inertial waves and wave instabilities in a spherical shell

Experimental survey of linear and nonlinear inertial waves and wave instabilities in a spherical shell

Non-axisymmetric instabilities in magnetic spherical Couette flow

Instabilities in magnetized spherical Couette flow

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