285 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
Differential rotation in fully convective stars
Under the assumption of thermal wind balance and effective entropy mixing in
constant rotation surfaces, the isorotational contours of the solar convective
zone may be reproduced with great fidelity. Even at this early stage of
development, this helioseismology fit may be used to put a lower bound on the
midlatitude {\em radial} solar entropy gradient, which in good accord with
standard mixing length theory. In this paper, we generalize this solar
calculation to fully convective stars (and potentially planets), retaining the
assumptions of thermal wind balance and effective entropy mixing in
isorotational surfaces. It is found that each isorotation contour is of the
form , where is the radius from the rotation axis,
is the (assumed spherical) gravitational potential, and and
are constant along the contour. This result is applied to simple models of
fully convective stars. Both solar-like surface rotation profiles (angular
velocity decreasing toward the poles) as well as "antisolar" profiles (angular
velocity increasing toward the poles) are modeled; the latter bear some
suggestive resemblance to numerical simulations. We also perform exploratory
studies of zonal surface flows similar to those seen in Jupiter and Saturn. In
addition to providing a practical framework for understanding the results of
large scale numerical simulations, our findings may also prove useful in
dynamical calculations for which a simple but viable model for the background
rotation profile in a convecting fluid is needed. Finally, our work bears
directly on an important goal of the CoRoT program: to elucidate the internal
structure of rotating, convecting stars.Comment: 21 pages, 20 figures. Accepted for publication in MNRA
Jump Rope Vortex in Liquid Metal Convection
Understanding large scale circulations (LSCs) in turbulent convective systems
is important for the study of stars, planets and in many industrial
applications. The canonical model of the LSC is quasi-planar with additional
horizontal sloshing and torsional modes [Brown E, Ahlers G (2009) J. Fluid
Mech. 638:383--400; Funfschilling D, Ahlers G (2004) Phys. Rev. Lett.
92(19):194502; Xi HD et al. (2009) Phys. Rev. Lett. 102(4):044503; Zhou Q et
al. (2009) J. Fluid Mech. 630:367--390]. Using liquid gallium as the working
fluid, we show via coupled laboratory-numerical experiments that the LSC in a
tank with aspect ratios greater than unity takes instead the form of a "jump
rope vortex", a strongly three-dimensional mode that periodically orbits around
the tank following a motion much like a jump rope on a playground. Further
experiments show that this jump rope flow also exists in more viscous fluids
such as water, albeit with a far smaller signal. Thus, this new jump rope mode
is an essential component of the turbulent convection that underlies our
observations of natural systems
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
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
Experimental study of internal wave generation by convection in water
We experimentally investigate the dynamics of water cooled from below at 0^oC
and heated from above. Taking advantage of the unusual property that water's
density maximum is at about 4^oC, this set-up allows us to simulate in the
laboratory a turbulent convective layer adjacent to a stably stratified layer,
which is representative of atmospheric and stellar conditions. High precision
temperature and velocity measurements are described, with a special focus on
the convectively excited internal waves propagating in the stratified zone.
Most of the convective energy is at low frequency, and corresponding waves are
localized to the vicinity of the interface. However, we show that some energy
radiates far from the interface, carried by shorter horizontal wavelength,
higher frequency waves. Our data suggest that the internal wave field is
passively excited by the convective fluctuations, and the wave propagation is
correctly described by the dissipative linear wave theory
Recommended from our members
The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration
published_or_final_versio
Oscillatory thermal-inertial flows in liquid metal rotating convection
We present the first detailed thermal and velocity field characterization of
convection in a rotating cylindrical tank of liquid gallium, which has
thermophysical properties similar to those of planetary core fluids. Our
laboratory experiments, and a closely associated direct numerical simulation,
are all carried out in the regime prior to the onset of steady convective
modes. This allows us to study the oscillatory convective modes, sidewall modes
and broadband turbulent flow that develop in liquid metals before the advent of
steady columnar modes. Our thermo-velocimetric measurements show that strongly
inertial, thermal wind flows develop, with velocities reaching those of
comparable non-rotating cases. Oscillatory bulk convection and wall modes
coexist across a wide range of our experiments, along with strong zonal flows
that peak in the Stewartson layer, but that extend deep into the fluid bulk in
the higher supercriticality cases. The flows contain significant time-mean
helicity that is anti-symmetric across the midplane, demonstrating that
oscillatory liquid metal convection contains the kinematic components to
sustain system-scale dynamo generation.Comment: 29 pages, 12 figure
A nonlinear model for rotationally constrained convection with Ekman pumping
It is a well established result of linear theory that the influence of
differing mechanical boundary conditions, i.e., stress-free or no-slip, on the
primary instability in rotating convection becomes asymptotically small in the
limit of rapid rotation. This is accounted for by the diminishing impact of the
viscous stresses exerted within Ekman boundary layers and the associated
vertical momentum transport by Ekman pumping. By contrast, in the nonlinear
regime recent experiments and supporting simulations are now providing evidence
that the efficiency of heat transport remains strongly influenced by Ekman
pumping in the rapidly rotating limit. In this paper, a reduced model is
developed for the case of low Rossby number convection in a plane layer
geometry with no-slip upper and lower boundaries held at fixed temperatures. A
complete description of the dynamics requires the existence of three distinct
regions within the fluid layer: a geostrophically balanced interior where fluid
motions are predominately aligned with the axis of rotation, Ekman boundary
layers immediately adjacent to the bounding plates, and thermal wind layers
driven by Ekman pumping in between. The reduced model uses a classical Ekman
pumping parameterization to alleviate the need for spatially resolving the
Ekman boundary layers. Results are presented for both linear stability theory
and a special class of nonlinear solutions described by a single horizontal
spatial wavenumber. It is shown that Ekman pumping allows for significant
enhancement in the heat transport relative to that observed in simulations with
stress-free boundaries. Without the intermediate thermal wind layer the
nonlinear feedback from Ekman pumping would be able to generate a heat
transport that diverges to infinity. This layer arrests this blowup resulting
in finite heat transport at a significantly enhanced value.Comment: 38 pages, 14 figure
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