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On the retrograde propagation of critical thermal convection in a slowly rotating spherical shell

Published online by Cambridge University Press:  16 July 2010

SHIN-ICHI TAKEHIRO
SHIN-ICHI TAKEHIRO*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
*
†Email address for correspondence: [email protected]
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Abstract

The retrograde propagation mechanism of critical thermal convection with a sectorial pattern emerging in a slowly rotating spherical shell is investigated through vorticity budget analysis. In the equatorial region, stretching and shrinking of the fluid columns in the direction of the axis of rotation due to the radial component of velocity causes retrograde propagation, whereas in the mid-latitudes, tilting of the radial component of planetary vorticity by the radial shear of the latitudinal component of velocity is dominant. The switching of the propagating direction from retrograde to prograde according to the increase in the rotation speed of the shell originates from the transition of the morphology of vortices from the ‘banana-shaped’ type due to the constraint of the spherical geometry to the columnar type due to the Taylor–Proudman constraint. The variation of the morphology of vortices reverses the tendency of stretching/shrinking of fluid columns accompanied by their cylindrically radial displacement.

JFM classification

Convection: Convection Geophysical and Geological Flows: Rotating flows Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 659 , 25 September 2010 , pp. 505 - 515
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Busse, F. H. 1970 a Differential rotation in stellar convection zones. Astrophys. J. 159, 629–639.CrossRefGoogle Scholar
Busse, F. H. 1970 b Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441–460.CrossRefGoogle Scholar
Busse, F. H. 1973 Differential rotation in stellar convection zones. Part II. Astron. Astrophys. 28, 27–37.Google Scholar
Busse, F. H. 1986 Asymptotic theory of convection in a rotating, cylindrical annulus. J. Fluid Mech. 173, 545–556.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hdromagnetic Stability. Oxford University Press, 652 pp.Google Scholar
Dormy, E., Soward, A. M., Jones, C. A., Jault, D. & Cardin, P. 2003 The onset of thermal convection in rotating spherical shells. J. Fluid Mech. 501, 43–70.CrossRefGoogle Scholar
Geiger, G. & Busse, F. H. 1981 On the onset of thermal convection in slowly rotating fluid shells. Geophys. Astrophys. Fluid Dyn. 18, 147–156.CrossRefGoogle Scholar
Gilman, P. A. 1975 Linear simulations of Boussinesq convection in a deep rotating spherical shell. J. Atmos. Sci. 32, 1331–1352.2.0.CO;2>CrossRefGoogle Scholar
Hirsching, W. R. & Yano, J.-I 1994 Metamorphosis of marginal thermal convection in rapidly rotating self-gravitating spherical shells. Geophys. Astrophys. Fluid Dyn. 74, 143–179.CrossRefGoogle Scholar
Jones, C. A., Soward, A. M. & Mussa, A. I. 2000 The onset of thermal convection in a rapidly rotating sphere. J. Fluid Mech. 405, 157–179.CrossRefGoogle Scholar
Roberts, P. H. 1968 On the thermal instability of a rotating-fluid sphere containing heat sources. Phil. Trans. R. Soc. Lond. A163, 93–117.Google Scholar
Takehiro, S. 2008 Physical interpretation of spiralling-columnar convection in a rapidly rotating annulus with radial propagation properties of Rossby waves. J. Fluid Mech. 614, 67–86.CrossRefGoogle Scholar
Takehiro, S. & Hayashi, Y.-Y 1995 Boussinesq convection in rotating spherical shells – a study on the equatorial superrotation. In The Earth's Central Part: Its Structure and Dymamics (ed. Yukutake, T.), pp. 123–156, TERAPUB.Google Scholar
Takehiro, S., Odaka, M., Ishioka, K., Ishiwatari, M., Hayashi, Y.-Y. & SPMODEL Development Group 2006 A series of hierarchical spectral models for geophyiscal fluid dynamics. Nagare Multimedia 2006, http://www.nagare.or.jp/mm/2006/spmodel/.Google Scholar
Yano, J.-I 1992 Asymptotic theory of thermal convection in rapidly rotating systems. J. Fluid Mech. 243, 103–131.CrossRefGoogle Scholar
Zhang, K. 1992 Spiralling columnar convection in rapidly rotating spherical fluid shells. J. Fluid Mech. 236, 535–556.CrossRefGoogle Scholar
Zhang, K. 1993 On equatorially trapped boundary inertial waves. J. Fluid Mech. 248, 203–217.CrossRefGoogle Scholar
Zhang, K. 1994 On coupling between the Poincare equation and the heat equation. J. Fluid Mech. 268, 211–229.CrossRefGoogle Scholar
Zhang, K.-K & Busse, F. H. 1987 On the onset of convection in rotating spherical shells. Geophys. Astrophys. Fluid Dyn. 39, 119–147.CrossRefGoogle Scholar