The influence of a sloping bottom endwall on the linear stability in the thermally driven baroclinic annulus with a free surface

  • Thomas von Larcher
  • Alexandre Fournier
  • Rainer Hollerbach
Original Article

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.

Keywords

Linear stability analysis Baroclinic instability Fourier–Legendre spectral element code Sloping bottom endwall Thermally driven rotating flows 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thomas von Larcher
    • 1
  • Alexandre Fournier
    • 2
  • Rainer Hollerbach
    • 3
    • 4
  1. 1.Institute for MathematicsFreie Universität BerlinBerlinGermany
  2. 2.Geomagnetism, Institut de Physique du Globe de Paris, Sorbonne Paris-CitéUniv Paris Diderot, UMR 7154 CNRSParisFrance
  3. 3.Institute of GeophysicsETH ZurichZurichSwitzerland
  4. 4.Department of Applied MathematicsUniversity of LeedsLeedsUK

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