456 research outputs found
Bistable flows in precessing spheroids
Precession driven flows are found in any rotating container filled with
liquid, when the rotation axis itself rotates about a secondary axis that is
fixed in an inertial frame of reference. Because of its relevance for planetary
fluid layers, many works consider spheroidal containers, where the uniform
vorticity component of the bulk flow is reliably given by the well-known
equations obtained by Busse in 1968. So far however, no analytical result on
the solutions is available. Moreover, the cases where multiple flows can
coexist have not been investigated in details since their discovery by Noir et
al. (2003). In this work, we aim at deriving analytical results on the
solutions, aiming in particular at, first estimating the ranges of parameters
where multiple solutions exist, and second studying quantitatively their
stability. Using the models recently proposed by Noir \& C{\'e}bron (2013),
which are more generic in the inviscid limit than the equations of Busse, we
analytically describe these solutions, their conditions of existence, and their
stability in a systematic manner. We then successfully compare these analytical
results with the theory of Busse (1968). Dynamical model equations are finally
proposed to investigate the stability of the solutions, which allows to
describe the bifurcation of the unstable flow solution. We also report for the
first time the possibility that time-dependent multiple flows can coexist in
precessing triaxial ellipsoids. Numerical integrations of the algebraic and
differential equations have been efficiently performed with the dedicated
script FLIPPER (supplementary material)
Precession-driven flows in non-axisymmetric ellipsoids
We study the flow forced by precession in rigid non-axisymmetric ellipsoidal
containers. To do so, we revisit the inviscid and viscous analytical models
that have been previously developed for the spheroidal geometry by,
respectively, Poincar\'e (Bull. Astronomique, vol. XXVIII, 1910, pp. 1-36) and
Busse (J. Fluid Mech., vol. 33, 1968, pp. 739-751), and we report the first
numerical simulations of flows in such a geometry. In strong contrast with
axisymmetric spheroids, where the forced flow is systematically stationary in
the precessing frame, we show that the forced flow is unsteady and periodic.
Comparisons of the numerical simulations with the proposed theoretical model
show excellent agreement for both axisymmetric and non-axisymmetric containers.
Finally, since the studied configuration corresponds to a tidally locked
celestial body such as the Earth's Moon, we use our model to investigate the
challenging but planetary-relevant limit of very small Ekman numbers and the
particular case of our Moon
Tidally driven dynamos in a rotating sphere
Large-scale planetary or stellar magnetic fields generated by a dynamo effect
are mostly attributed to flows forced by buoyancy forces in electrically
conducting fluid layers. However, these large-scale fields may also be
controlled by tides, as previously suggested for the star -boo, Mars or
the Early Moon. By simulating a small local patch of a rotating fluid,
\cite{Barker2014} have recently shown that tides can drive small-scale dynamos
by exciting a hydrodynamic instability, the so-called elliptical (or tidal)
instability. By performing global magnetohydrodynamic simulations of a rotating
spherical fluid body, we investigate if this instability can also drive the
observed large-scale magnetic fields. We are thus interested by the dynamo
threshold and the generated magnetic field in order to test if such a mechanism
is relevant for planets and stars. Rather than solving the problem in a
geometry deformed by tides, we consider a spherical fluid body and add a body
force to mimic the tidal deformation in the bulk of the fluid. This allows us
to use an efficient spectral code to solve the magnetohydrodynamic problem. We
first compare the hydrodynamic results with theoretical asymptotic results, and
numerical results obtained in a truely deformed ellipsoid, which confirms the
presence of the elliptical instability. We then perform magnetohydrodynamic
simulations, and investigate the dynamo capability of the flow. Kinematic and
self-consistent dynamos are finally simulated, showing that the elliptical
instability is capable of generating dipole dominated large-scale magnetic
field in global simulations of a fluid rotating sphere.Comment: Astrophysical Journal Letters In press, (accepted) (2014) (accepted
Spontaneous generation of inertial waves from boundary turbulence in a librating sphere
In this work, we report the excitation of inertial waves in a librating
sphere even for libration frequencies where these waves are not directly
forced. This spontaneous generation comes from the localized turbulence induced
by the centrifugal instabilities in the Ekman boundary layer near the equator
and does not depend on the libration frequency. We characterize the key
features of these inertial waves in analogy with previous studies of the
generation of internal waves in stratified flows from localized turbulent
patterns. In particular, the temporal spectrum exhibits preferred values of
excited frequency. This first-order phenomenon is generic to any rotating flow
in the presence of localized turbulence and is fully relevant for planetary
applications
Precession-driven flows in non-axisymmetric ellipsoids
International audienceWe study the flow forced by precession in rigid non-axisymmetric ellipsoidal containers. To do so, we revisit the inviscid and viscous analytical models that have been previously developed for the spheroidal geometry by, respectively, Poincaré (Bull. Astronomique, vol. XXVIII, 1910, pp. 1-36) and Busse (J. Fluid Mech., vol. 33, 1968, pp. 739-751), and we report the first numerical simulations of flows in such a geometry. In strong contrast with axisymmetric spheroids, where the forced flow is systematically stationary in the precessing frame, we show that the forced flow is unsteady and periodic. Comparisons of the numerical simulations with the proposed theoretical model show excellent agreement for both axisymmetric and non-axisymmetric containers. Finally, since the studied configuration corresponds to a tidally locked celestial body such as the Earth's Moon, we use our model to investigate the challenging but planetary-relevant limit of very small Ekman numbers and the particular case of our Moon
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