Non-axisymmetric instabilities in magnetic spherical Couette flow. (English) Zbl 1186.76651
Summary: 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.
MSC:
| 76E25 | Stability and instability of magnetohydrodynamic and electrohydrodynamic flows |
| 76E07 | Rotation in hydrodynamic stability |
| 76U05 | General theory of rotating fluids |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
References:
| [1] | EARTH PLANET SCI LETT 160 pp 15– (1998) |
| [2] | PROC R SOC LOND A 444 pp 333– (1994) |
| [3] | INT J NUMER METHODS FLUIDS 32 pp 773– (2000) |
| [4] | PROC R SOC LOND A 457 pp 785– (2001) |
| [5] | FLUID DYNAM RES 38 pp 257– (2006) |
| [6] | EUR J MECH B 26 pp 729– (2007) |
| [7] | PHILOS MAG 42 pp 1308– (1951) · doi:10.1080/14786444108561386 |
| [8] | J FLUID MECHANICS 344 pp 213– (1997) |
| [9] | J FLUID MECHANICS 93 pp 515– (1979) |
| [10] | GEOPHYS ASTROPHYS FLUID DYNAM 100 pp 281– (2006) |
| [11] | PHYS EARTH PLANET INT 170 pp 60– (2008) |
| [12] | Sisan, Physical Review Letters 93 (11) pp 114502– (2004) · doi:10.1103/PhysRevLett.93.114502 |
| [13] | PHYS FLUIDS 10 pp 2412– (1998) |
| [14] | J FLUID MECHANICS 389 pp 81– (1999) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
