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On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions

  • MARTA NET (a1), FERRAN GARCIA (a1) and JUAN SÁNCHEZ (a1)
Abstract

Accurate numerical computations of the onset of thermal convection in wide rotating spherical shells are presented. Low-Prandtl-number (σ) fluids, and non-slip boundary conditions are considered. It is shown that at small Ekman numbers (E), and very low σ values, the well-known equatorially trapped patterns of convection are superseded by multicellular outer-equatorially-attached modes. As a result, the convection spreads to higher latitudes affecting the body of the fluid, and increasing the internal viscous dissipation. Then, from E < 10−5, the critical Rayleigh number (Rc) fulfils a power-law dependence Rc ~ E−4/3, as happens for moderate and high Prandtl numbers. However, the critical precession frequency (|ωc|) and the critical azimuthal wavenumber (mc) increase discontinuously, jumping when there is a change of the radial and latitudinal structure of the preferred eigenfunction. In addition, the transition between spiralling columnar (SC), and outer-equatorially-attached (OEA) modes in the (σ, E)-space is studied. The evolution of the instability mechanisms with the parameters prevents multicellular modes being selected from σ≳0.023. As a result, and in agreement with other authors, the spiralling columnar patterns of convection are already preferred at the Prandtl number of the liquid metals. It is also found that, out of the rapidly rotating limit, the prograde antisymmetric (with respect to the equator) modes of small mc can be preferred at the onset of the primary instability.

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F. Al-Shamali , M. Heimpel & J. Arnou 2004 Varying the spherical shell geometry in rotating thermal convection. Geophys. Astrophys. Fluid Dyn. 98, 153169.

J. Aubert , D. Brito , H.-C. Nataf , P. Cardin & J. P. Masson 2001 A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium. Phys. Earth Planet. Inter. 128, 5174.

O. Batiste , I. Mercader , M. Net & E. Knobloch 1999 Onset of oscillatory binary fluid convection in finite containers. PRE 59, 67306741.

R. E. Ecke , F. Zhong & E. Knobloch 1992 Hopf bifurcation with broken reflection symmetry in rotating Rayleigh–Bénard convection. Europhys. Lett. 19, 177182.

C. C. Finlay & A. Jackson 2003 Equatorially dominated magnetic field change at the surface of the Earth's core. Science 300 (5628), 20842086.

N. Gillet , D. Brito , D. Jault & H.-C. Nataf 2007 Experimental and numerical studies of convection in a rapidly rotating spherical shell. J. Fluid Mech. 580, 83121.

R. B. Lehoucq , D. C. Sorensen & C. Yang 1998 ARPACK User's Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM.

P. H. Roberts 1968 On the thermal instability of a rotating fluid sphere containing heat sources. Phil. Trans. R. Soc. Lond. A 263, 93117.

R. A. Secco & H. H. Schloessin 1989 The electrical resistivity of solid and liquid Fe at pressures up to 7 GPa. J. Geophy. Res. B 94, 58875894.

R. Simitev & F. H. Busse 2003 Patterns of convection in rotating spherical shells. New J. Phys. 5, 97.197.20.

A. M. Soward 1977 On the finite amplitude thermal instability in a rapidly rotating fluid sphere. Geophys. Astrophys. Fluid Dyn. 9, 1974.

K. Zhang & F. H. Busse 1987 On the onset of convection in rotating spherical shells. Geophys. Astrophys. Fluid Dyn. 39, 119147.

K. Zhang & C. A. Jones 1993 The influence of Ekman boundary layers on rotating convection. Geophys. Astrophys. Fluid Dyn. 71, 145162.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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