Journal ArticleDOI
Onset of convection in a rapidly rotating compressible fluid spherical shell
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In this paper, a rapidly rotating compressible fluid spherical shell is considered and the effect of introducing compressibility for different choices of the Prandtl number, Pr, comparing their results with those for a similar model of Glatzmaier and Gilman.Abstract:
We consider a rapidly rotating compressible fluid spherical shell, and study linear perturbations of a polytropic equilibrium state. Instead of considering the fully compressible problem, we make the anelastic approximation. We start from Boussinesq solutions and study the effect of introducing compressibility for different choices of the Prandtl number, Pr, comparing our results with those for a similar model of Glatzmaier and Gilman (1981). For Pr = 1 and 10, the results are similar. As compressibility is increased, convection becomes localised near to the inner boundary, an effect which is magnified by increasing the rotation rate. When we consider Pr = 0.1 we find different results. As compressibility is introduced, the critical Rayleigh number, R c decreases sharply and becomes negative. This behaviour was not found by Glatzmaier and Gilman.read more
Citations
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Compressible convection in the deep atmospheres of giant planets
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Linear theory of compressible convection in rapidly rotating spherical shells, using the anelastic approximation
TL;DR: In this paper, the authors studied the onset of compressible convection in rapidly rotating spherical shells and developed an asymptotic theory valid at low Ekman number and compared with numerical solutions of the full equations.
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Energy conservation and gravity waves in sound-proof treatments of stellar interiors. part i. anelastic approximations
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Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations
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References
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Journal ArticleDOI
Thermal instabilities in rapidly rotating systems
TL;DR: In this paper, the Taylor-Proudman theorem is applied to describe the instability of the lower symmetric regime of a self-gravitating, internally heated, rotating fluid sphere.
Journal ArticleDOI
On the thermal instability of a rotating-fluid sphere containing heat sources
TL;DR: The theory of marginal convection in a uniformly rotating, self-gravitating, fluid sphere, of uniform density and containing a uniform distribution of heat sources, is developed to embrace modes of convection which are asymmetric with respect to the axis of rotation.
Journal ArticleDOI
Spiralling columnar convection in rapidly rotating spherical fluid shells
TL;DR: In this paper, it was shown that the fundamental features of both thermal instabilities and the corresponding nonlinear convection in rapidly rotating spherical systems (in the range of the Taylor number 109 < T < 1012) are determined by the fluid properties characterized by the size of the Prandtl number.
Journal ArticleDOI
Compressible convection in a rotating spherical shell. I - Anelastic equations. II - A linear anelastic model. III - Analytic model for compressible vorticity waves
P. A. Gilman,G. A. Glatzmaier +1 more
TL;DR: In this paper, the authors derived anelastic equations for convection of a compressible fluid in a deep rotating spherical shell, which can help us understand what role the large density variation present in the solar convection zone plays in the maintenance of the solar differential rotation through angular momentum transports by global scale convection.
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