Journal ArticleDOI
Low-Prandtl-number convection in a rotating cylindrical annulus
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In this paper, a boundary layer theory is presented which allows a systematic study of the linear properties of the system in the asymptotic regime of very fast rotation rates, and the influence of this global coupling term on the sideband instabilities of the waves is studied.Abstract:
Motivated by recent experimental results obtained in a low-Prandtl-number fluid (Jaletzky 1999), we study theoretically the rotating cylindrical annulus model with rigid boundary conditions. A boundary layer theory is presented which allows a systematic study of the linear properties of the system in the asymptotic regime of very fast rotation rates. It shows that the Stewartson layers have a (de)stabilizing influence at (high) low Prandtl numbers. In the weakly nonlinear regime and for low Prandtl numbers, a strong retrograde mean flow develops at quadratic order. The Poiseuille part of this mean flow is determined by an equation obtained by averaging of the Navier-Stokes equation. It thus gives rise to a new global-coupling term in the envelope equation describing modulated waves, which can be used for other systems. The influence of this global-coupling term on the sideband instabilities of the waves is studied. In the strongly nonlinear regime, the waves restabilize against these instabilities at small rotation rates, but they are destabilized by a short-wavelength mode at larger rotation rates. We also find an inversion in the dependence of the amplitude on the Rayleigh number at low Prandtl numbers and intermediate rotation rates.read more
Citations
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Journal ArticleDOI
A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium
TL;DR: In this paper, the results of finite-amplitude convection experiments in a rotating spherical shell are presented, where water (Prandtl number P = 7) and liquid gallium (P = 0027) have been used as working fluids.
Book ChapterDOI
Thermal and Compositional Convection in the Outer Core
TL;DR: In this paper, the Earth's liquid outer core is stirred by thermal and compositional convection, and the issues of how fast the convective motions are, what is their morphology, and how this relates to the heat transport are discussed.
Journal ArticleDOI
The quasi-geostrophic model for rapidly rotating spherical convection outside the tangent cylinder
Nicolas Gillet,Chris A. Jones +1 more
TL;DR: In this paper, a quasi-geostrophic approximation of the Prandtl-number dependence of rapidly rotating convection in spherical geometry outside the tangent cylinder is investigated using quasi geostrophic approximations.
Journal ArticleDOI
Turbulent convection in liquid metal with and without rotation
Eric M. King,Jonathan M. Aurnou +1 more
TL;DR: In general, it is found that the convective behavior of liquid metal differs substantially from that of moderate fluids, such as water, and this difference may explain the different classes of magnetic fields observed on the Gas and Ice Giant planets.
Journal ArticleDOI
Experimental and numerical studies of convection in a rapidly rotating spherical shell
TL;DR: In this article, thermal convection in a rapidly rotating spherical shell is investigated experimentally and numerically, and a scaling law U ∼ 4/3 is derived and verified both numerically and experimentally.
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
High Rayleigh number β-convection
TL;DR: In this article, high-resolution numerical simulations of thermal convection in a rapidly rotating channel with gravity perpendicular to the rotation vector are described, and the convecting columns are subject to a β-effect resulting from topographic vortex stretching.
Journal ArticleDOI
Convection in a rotating cylindrical annulus: thermal Rossby waves
Friedrich H. Busse,A. C. Or +1 more
TL;DR: In this article, it is shown that even in the absence of curvature of the surfaces bounding the fluid annulus in the axial direction, a mean flow is generated by Reynolds stresses.
Journal ArticleDOI
Pattern selection in rotating convection with experimental boundary conditions.
T. Clune,Edgar Knobloch +1 more
TL;DR: In this article, the critical rotation rate beyond which rolls are Kuppers-Lortz unstable as well as the angle with which the instability sets in are computed. But the results differ considerably from those with more idealized boundary conditions.