Journal ArticleDOI
Steady fluid flow in a precessing spheroidal shell
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TLDR
In this article, the linear boundary-layer analysis for the motion of a viscous fluid inside the spheroidal cavity of a precessing rigid body is extended to include effects due to the nonlinear terms in the boundary layer equation, resulting in a differential rotation superimposed on the constant vorticity flow given by the linear theory.Abstract:
The linear boundary-layer analysis by Stewartson & Roberts (1963) and by Roberts & Stewartson (1965) for the motion of a viscous fluid inside the spheroidal cavity of a precessing rigid body is extended to include effects due to the nonlinear terms in the boundary-layer equation. The most significant consequence is a differential rotation super-imposed on the constant vorticity flow given by the linear theory. In addition it is shown that a tidal bulge of the cavity forces a fluid motion similar to that caused by the precessional torque. The relevance of both effects for the liquid core of the earth is briefly discussed.read more
Citations
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Long term evolution and chaotic diffusion of the insolation quantities of Mars
Jacques Laskar,Alexandre C. M. Correia,Alexandre C. M. Correia,Mickael Gastineau,F. Joutel,Benjamin Levrard,Philippe Robutel +6 more
TL;DR: In this paper, the authors used the most recent data for the rotational state of Mars, and a new numerical integration of the Solar System, to provide a precise solution for the evolution of Mars' spin over 10 to 20 Myr.
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Geodesy by radio interferometry: Studies of the forced nutations of the Earth: 2. Interpretation
Journal ArticleDOI
Hydromagnetics of rotating fluids
David Acheson,Raymond Hide +1 more
TL;DR: In this paper, the dynamics of a rapidly rotating electrically conducting fluid in the presence of a corotating magnetic field are studied. But the authors focus on the dynamics in the case of a single magnetic field.
Journal ArticleDOI
Precession driven dynamos
TL;DR: In this article, the dynamo effect is demonstrated numerically in precession driven flow in a spherical container, where both laminar as well as unstable flows act as dynamos.
References
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Journal ArticleDOI
Free Hydromagnetic Oscillations of the Earth's Core and the Theory of the Geomagnetic Secular Variation
TL;DR: In this article, free hydromagnetic oscillations of a rotating spherical shell of an incompressible fluid are investigated by means of a simple theoretical model for each spatial harmonic, rotation gives rise to two distinct modes of oscillation, "magnetic" and "inertial" which propagate with different velocities.
Journal ArticleDOI
On the motion of liquid in a spheroidal cavity of a precessing rigid body
K. Stewartson,P. H. Roberts +1 more
TL;DR: In this paper, the authors examined the flow set up in an oblate cavity of a precessing rigid body under the assumptions that the ellipticity of the spheroidal boundary of the fluid is large compared with Ω/ω and that the boundary-layer thickness is small compared with the deviations of the boundary from sphericity.
Journal ArticleDOI
On the stability of a maclaurin spheroid of small viscosity
P. H. Roberts,K. Stewartson +1 more
TL;DR: In this article, the stability of a viscous MacLaurin spheroid is solved asymptotically for small kinematic viscosity, nu, and it is shown that, in this limit, the frequency of oscillation, n, with respect to the mode which becomes neutrally stable at the point of bifurcation (where the eccentricity, e, of the meridional section is approximately 0.8127), is n=n sub o + (5 nu (n sub 0)sq)/(phi(e)) + O
Journal ArticleDOI
On the transient motion of a contained rotating fluid
TL;DR: In this paper, the authors considered the transient motion of a viscous fluid in a container rotating with constant angular velocity and studied the effects of viscosity on the rotation of the container.
Journal ArticleDOI
On the motion of a liquid in a spheroidal cavity of a precessing rigid body. II
P. H. Roberts,K. Stewartson +1 more
TL;DR: In this paper, it was shown that the problem of finding the ultimate state of motion of a viscous incompressible fluid relative to the container can be solved for arbitrary e (including zero) under the assumption that the kinematic viscosity of the fluid is unknown.
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