Instabilities of Taylor columns in a rotating stratified fluid. (English) Zbl 1233.76112
Summary: We numerically solve for the flow in a differentially rotating spherical shell, with a stable stratification imposed along the rotation axis. The axisymmetric basic state evolves from a Stewartson layer in the unstratified limit to a Taylor column in the strongly stratified limit. For the Taylor columns, we next compute the linear onset of non-axisymmetric instabilities, and show that small (0.1) and large (10) Prandtl numbers yield very different results. For \(\mathrm{Pr}=10\), positive and negative differential rotations also yield fundamentally different instabilities.
MSC:
| 76U05 | General theory of rotating fluids |
| 76F45 | Stratification effects in turbulence |
| 76E07 | Rotation in hydrodynamic stability |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
References:
| [1] | Taylor, G. I., Proc. R. Soc. London A, 104, 213 (1923) |
| [2] | Boyer, D. L.; Davies, P. A., Annu. Rev. Fluid Mech., 32, 165 (2000) · Zbl 0953.76513 |
| [3] | Meredith, M. P.; Watkins, J. L.; Murphy, E. J.; Cunningham, N. J.; Wood, A. G.; Korb, R.; Whitehouse, M. J.; Thorpe, S. E.; Vivier, F., Geophys. Res. Lett., 30, 2061 (2003) |
| [4] | Adduce, C.; Cenedese, C., J. Marine Res., 62, 611 (2004) |
| [5] | Moore, G. W.K.; Semple, J. L., Geophys. Res. Lett., 32, L21810 (2005) |
| [6] | Stewartson, K., J. Fluid Mech., 26, 131 (1966) · Zbl 0139.44102 |
| [7] | Hollerbach, R., Proc. R. Soc. London A, 444, 333 (1994) · Zbl 0807.76095 |
| [8] | Dormy, E.; Cardin, P.; Jault, D., Earth Planet Sci. Lett., 160, 15 (1998) |
| [9] | Früh, W. G.; Read, P. L., J. Fluid Mech., 383, 143 (1999) · Zbl 0941.76531 |
| [10] | Hollerbach, R., J. Fluid Mech., 492, 289 (2003) · Zbl 1063.76558 |
| [11] | Hollerbach, R.; Futterer, B.; More, T.; Egbers, C., Theor. Comp. Fluid Dynam., 18, 197 (2004) · Zbl 1179.76034 |
| [12] | Schaeffer, N.; Cardin, P., Phys. Fluids, 17, 104111 (2005) · Zbl 1188.76138 |
| [13] | Greenspan, H. P., The Theory of Rotating Fluids (1968), Cambridge University Press · Zbl 0182.28103 |
| [14] | Hollerbach, R., Int. J. Numer. Meth. Fluids, 32, 773 (2000) · Zbl 0958.76065 |
| [15] | Killworth, P. D., Dynam. Atmos. Oceans, 4, 143 (1980) |
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.
