von Larcher, T. and Fournier, A. and Hollerbach, R.
(2013)
*The influence of a sloping bottom endwall on the linear stability in the thermally driven baroclinic annulus with a free surface.*
Theoretical and Computational Fluid Dynamics , 27
(3-4).
pp. 433-451.
ISSN Print: 0935-4964; Online: 1432-2250

Full text not available from this repository.

Official URL: http://link.springer.com/article/10.1007%2Fs00162-...

## Abstract

We present results of a linear stability analysis of non-axisymmetric thermally driven flows in the classical model of the rotating cylindrical gap of fluid with a horizontal temperature gradient [inner (outer) sidewall cool (warm)] and a sloping bottom endwall configuration where fluid depth increases with radius. For comparison, results of a flat-bottomed endwall case study are also discussed. In both cases, the model setup has a free top surface. The analysis is carried out numerically using a Fourier–Legendre spectral element method (in azimuth and in the meridional plane, respectively) well suited to handle the axisymmetry of the fluid container. We find significant differences between the neutral stability curve for the sloping and the flat-bottomed endwall configuration. In case of a sloping bottom endwall, the wave flow regime is extended to lower rotation rates, that is, the transition curve is shifted systematically to lower Taylor numbers. Moreover, in the sloping bottom endwall case, a sharp reversal of the instability curve is found in its upper part, that is, at large temperature differences, whereas the instability line becomes almost horizontal in the flat-bottomed endwall case. The linear onset of instability is then almost independent of the rotation rate.

Item Type: | Article |
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Uncontrolled Keywords: | Linear stability analysis, Baroclinic instability,Fourier–Legendre spectral element code,Sloping bottom endwall, Thermally driven rotating flows |

Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group |

ID Code: | 1089 |

Deposited By: | Ulrike Eickers |

Deposited On: | 30 Aug 2011 12:27 |

Last Modified: | 14 Jun 2013 14:19 |

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