86 research outputs found
Zonal flow regimes in rotating anelastic spherical shells: an application to giant planets
The surface zonal winds observed in the giant planets form a complex jet
pattern with alternating prograde and retrograde direction. While the main
equatorial band is prograde on the gas giants, both ice giants have a
pronounced retrograde equatorial jet.
We use three-dimensional numerical models of compressible convection in
rotating spherical shells to explore the properties of zonal flows in different
regimes where either rotation or buoyancy dominates the force balance. We
conduct a systematic parameter study to quantify the dependence of zonal flows
on the background density stratification and the driving of convection.
We find that the direction of the equatorial zonal wind is controlled by the
ratio of buoyancy and Coriolis force. The prograde equatorial band maintained
by Reynolds stresses is found in the rotation-dominated regime. In cases where
buoyancy dominates Coriolis force, the angular momentum per unit mass is
homogenised and the equatorial band is retrograde, reminiscent to those
observed in the ice giants. In this regime, the amplitude of the zonal jets
depends on the background density contrast with strongly stratified models
producing stronger jets than comparable weakly stratified cases. Furthermore,
our results can help to explain the transition between solar-like and
"anti-solar" differential rotations found in anelastic models of stellar
convection zones.
In the strongly stratified cases, we find that the leading order force
balance can significantly vary with depth (rotation-dominated inside and
buoyancy-dominated in a thin surface layer). This so-called "transitional
regime" has a visible signature in the main equatorial jet which shows a
pronounced dimple where flow amplitudes notably decay towards the equator. A
similar dimple is observed on Jupiter, which suggests that convection in the
planet interior could possibly operate in this regime.Comment: 20 pages, 15 figures, 4 tables, accepted for publication in Icaru
Turbulent Rayleigh-B\'enard convection in spherical shells
We simulate numerically Boussinesq convection in non-rotating spherical
shells for a fluid with a unity Prandtl number and Rayleigh numbers up to
. In this geometry, curvature and radial variations of the gravitationnal
acceleration yield asymmetric boundary layers. A systematic parameter study for
various radius ratios (from to ) and gravity
profiles allows us to explore the dependence of the asymmetry on these
parameters. We find that the average plume spacing is comparable between the
spherical inner and outer bounding surfaces. An estimate of the average plume
separation allows us to accurately predict the boundary layer asymmetry for the
various spherical shell configurations explored here. The mean temperature and
horizontal velocity profiles are in good agreement with classical
Prandtl-Blasius laminar boundary layer profiles, provided the boundary layers
are analysed in a dynamical frame, that fluctuates with the local and
instantaneous boundary layer thicknesses. The scaling properties of the Nusselt
and Reynolds numbers are investigated by separating the bulk and boundary layer
contributions to the thermal and viscous dissipation rates using numerical
models with and a gravity proportional to . We show that our
spherical models are consistent with the predictions of Grossmann \& Lohse's
(2000) theory and that and scalings are in good agreement
with plane layer results.Comment: 43 pages, 25 figures, 2 tables, accepted for publication in JF
Libration driven elliptical instability
The elliptical instability is a generic instability which takes place in any
rotating flow whose streamlines are elliptically deformed. Up to now, it has
been widely studied in the case of a constant, non-zero differential rotation
between the fluid and the elliptical distortion with applications in
turbulence, aeronautics, planetology and astrophysics. In this letter, we
extend previous analytical studies and report the first numerical and
experimental evidence that elliptical instability can also be driven by
libration, i.e. periodic oscillations of the differential rotation between the
fluid and the elliptical distortion, with a zero mean value. Our results
suggest that intermittent, space-filling turbulence due to this instability can
exist in the liquid cores and sub-surface oceans of so-called synchronized
planets and moons
A Heuristic Framework for Next-Generation Models of Geostrophic Convective Turbulence
Many geophysical and astrophysical phenomena are driven by turbulent fluid
dynamics, containing behaviors separated by tens of orders of magnitude in
scale. While direct simulations have made large strides toward understanding
geophysical systems, such models still inhabit modest ranges of the governing
parameters that are difficult to extrapolate to planetary settings. The
canonical problem of rotating Rayleigh-B\'enard convection provides an
alternate approach - isolating the fundamental physics in a reduced setting.
Theoretical studies and asymptotically-reduced simulations in rotating
convection have unveiled a variety of flow behaviors likely relevant to natural
systems, but still inaccessible to direct simulation. In lieu of this, several
new large-scale rotating convection devices have been designed to characterize
such behaviors. It is essential to predict how this potential influx of new
data will mesh with existing results. Surprisingly, a coherent framework of
predictions for extreme rotating convection has not yet been elucidated. In
this study, we combine asymptotic predictions, laboratory and numerical
results, and experimental constraints to build a heuristic framework for
cross-comparison between a broad range of rotating convection studies. We
categorize the diverse field of existing predictions in the context of
asymptotic flow regimes. We then consider the physical constraints that
determine the points of intersection between flow behavior predictions and
experimental accessibility. Applying this framework to several upcoming devices
demonstrates that laboratory studies may soon be able to characterize
geophysically-relevant flow regimes. These new data may transform our
understanding of geophysical and astrophysical turbulence, and the conceptual
framework developed herein should provide the theoretical infrastructure needed
for meaningful discussion of these results.Comment: 36 pages, 8 figures. CHANGES: in revision at Geophysical and
Astrophysical Fluid Dynamic
Experimental study of libration-driven zonal flows in non-axisymmetric containers
International audienceOrbital dynamics that lead to longitudinal libration of celestial bodies also result in an elliptically deformed equatorial core-mantle boundary. The non-axisymmetry of the boundary leads to a topographic coupling between the assumed rigidmantle and the underlying low viscosity fluid.The present experimental study investigates theeffect of non axisymmetric boundaries on the zonal flow driven by longitudinal libration. For large enough equatorial ellipticity, we report intermittent space-filling turbulence in particular bands of resonant frequency correlated with larger amplitude zonal flow. The mechanism underlying the intermittent turbulence has yet to be unambiguously determined. Nevertheless, recent numerical simulations in triaxial and biaxial ellipsoids suggest that it may be associated with the growth and collapse of an elliptical instability (Cebron et al., 2012). Outside of the band of resonance, we find that the background flow is laminar and the zonal flow becomes independent of the geometry at first order, in agreement with a non linear mechanism in the Ekman boundary layer (e.g. Calkins et al.; 2010, Sauret and Le Dizes, 2012b)
Génération d'ondes gravito-inertielles par la turbulence
Dans de nombreuses situations géophysiques et astrophysiques, une couche de fluide turbulent se situe au dessus ou en-dessous d'une zone stratifiée stable. C'est par exemple le cas des zones convective et radiative des étoiles. Alors que cette zone stratifiée a longtemps été assimilée à une zone immobile, il s'avère qu'elle est en fait le siège de mouvements oscillatoires (ondes gravito- inertielles) excités par la turbulence voisine. Ces ondes sont susceptibles de transporter de la quantité de mouvement et de l'énergie, donc d'influer significativement sur la dynamique du système considéré. Il est donc primordial de comprendre leur génération et leurs caractéristiques
Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers versus Interior Dynamics
Rapidly rotating Rayleigh-BĂ©nard convection is studied by combining results from direct numerical simulations (DNS), laboratory experiments, and asymptotic modeling. The asymptotic theory is shown to provide a good description of the bulk dynamics at low, but finite Rossby number. However, large deviations from the asymptotically predicted heat transfer scaling are found, with laboratory experiments and DNS consistently yielding much larger Nusselt numbers than expected. These deviations are traced down to dynamically active Ekman boundary layers, which are shown to play an integral part in controlling heat transfer even for Ekman numbers as small as 10^{-7}. By adding an analytical parametrization of the Ekman transport to simulations using stress-free boundary conditions, we demonstrate that the heat transfer jumps from values broadly compatible with the asymptotic theory to states of strongly increased heat transfer, in good quantitative agreement with no-slip DNS and compatible with the experimental data. Finally, similarly to nonrotating convection, we find no single scaling behavior, but instead that multiple well-defined dynamical regimes exist in rapidly rotating convection systems
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