The influence of a sloping bottom endwall on the linear stability in the thermally driven baroclinic annulus with a free surface
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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.
KeywordsLinear stability analysis Baroclinic instability Fourier–Legendre spectral element code Sloping bottom endwall Thermally driven rotating flows
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- 10.Früh, W.G., Maubert, P., Read, P., Randriamampianina, A.: DNS of structural vacillation in the transition to geostrophic turbulence. In: Palma J., Lopes A.S. (eds.) Advances in Turbulence XI, Proceedings in Physics, vol. 117, pp. 432–434. Springer (2007)Google Scholar
- 13.Fultz, D.: Development in controlled experiments on larger scale geophysical problems. In: Advances in Geophysics, vol. 7, pp. 1–104. Academic Press (1961)Google Scholar
- 16.Hide R.: Some laboratory experiments on free thermal convection in a rotating fluid subject to a horizontal temperature gradient and their relation to the theory of the global atmospheric circulation. In: Corby, G. (ed.) The global circulation of the atmosphere, pp. 196–221. R. Met. Office, London (1969)Google Scholar
- 27.Marschall J., Plumb R.A.: Atmosphere, Ocean, and Climate Dynamics. Elsevier Academic Press, USA (2008)Google Scholar
- 31.Read P.L.: Rotating annulus flows and baroclinic waves. In: Hopfinger, E. (ed.) Rotating Fluids in Geophysical and Industrial Applications, pp. 185–214. Springer, Wien-New York (1992)Google Scholar
- 38.Veronis G.: On the approximation involved in transforming the equations of motion from a spherical surface onto a β-plane-plane. J. Mar. Res. 21, 110–124 (1963)Google Scholar
- 40.White A.A.: The dynamics of rotating fluids: numerical modelling of annulus flows. Met. Mag. 117, 54–63 (1988)Google Scholar
- 43.Wordsworth, R.D., Read, P.L., Yamazaki, Y.H.: Turbulence, waves, and jets in a differentially heated rotating annulus experiment. Phys. Fluids 20, doi: 10.1063/1.2990,042 (2008)