2,984 research outputs found
A hemispherical dynamo model : Implications for the Martian crustal magnetization
Mars Global Surveyor measurements revealed that the Martian crust is strongly
magnetized in the southern hemisphere while the northern hemisphere is
virtually void of magnetization. Two possible reasons have been suggested for
this dichotomy: A once more or less homogeneously magnetization may have been
destroyed in the northern hemisphere by, for example, resurfacing or impacts.
The alternative theory we further explore here assumes that the dynamo itself
produced a hemispherical field. We use numerical dynamo simulations to study
under which conditions a spatial variation of the heat flux through the
core-mantle boundary (CMB) may yield a strongly hemispherical surface field. We
assume that the early Martian dynamo was exclusively driven by secular cooling
and we mostly concentrate on a cosine CMB heat flux pattern with a minimum at
the north pole, possibly caused by the impacts responsible for the northern
lowlands. This pattern consistently triggers a convective mode which is
dominated by equatorially anti-symmetric and axisymmetric (EAA) thermal winds.
Convective up- and down-wellings and thus radial magnetic field production then
tend to concentrate in the southern hemisphere which is still cooled
efficiently while the northern hemisphere remains hot. The dynamo changes from
an alpha^2- for a homogeneous CMB heat flux to an alpha-Omega-type in the
hemispherical configuration. These dynamos reverse on time scales of about 10
kyrs. This too fast to allow for the more or less unidirectional magnetization
of thick crustal layer required to explain the strong magnetization in the
southern hemisphere
A Gaussian Model for Simulated Geomagnetic Field Reversals
Field reversals are the most spectacular changes in the geomagnetic field but
remain little understood. Paleomagnetic data primarily constrain the reversal
rate and provide few additional clues. Reversals and excursions are
characterized by a low in dipole moment that can last for some 10kyr. Some
paleomagnetic records also suggest that the field decreases much slower before
an reversals than it recovers afterwards and that the recovery phase may show
an overshoot in field intensity. Here we study the dipole moment variations in
several extremely long dynamo simulation to statistically explored the reversal
and excursion properties. The numerical reversals are characterized by a switch
from a high axial dipole moment state to a low axial dipole moment state. When
analysing the respective transitions we find that decay and growth have very
similar time scales and that there is no overshoot. Other properties are
generally similar to paleomagnetic findings. The dipole moment has to decrease
to about 30% of its mean to allow for reversals. Grand excursions during which
the field intensity drops by a comparable margin are very similar to reversals
and likely have the same internal origin. The simulations suggest that both are
simply triggered by particularly large axial dipole fluctuations while other
field components remain largely unaffected. A model at a particularly large
Ekman number shows a second but little Earth-like type of reversals where the
total field decays and recovers after some time
Penetrative Convection in Partly Stratified Rapidly Rotating Spherical Shells
Celestial objects host interfaces between convective and stable stratified
interior regions. The interaction between both, e.g., the transfer of heat,
mass, or angular momentum depends on whether and how flows penetrate into the
stable layer. Powered from the unstable, convective regions, radial flows can
pierce into the stable region depending on their inertia (overshooting). In
rapidly rotating systems, the dynamics are strongly influenced by the Coriolis
force and radial flows penetrate in stratified regions due to the geostrophic
invariance of columnar convection even in the limit of vanishing inertia.
Within this study, we numerically investigate both mechanisms and hence explore
the nature of penetrative convection in rapidly rotating spherical shells. The
study covers a broad range of system parameters, such as the strength of the
stratification relative to the Coriolis force or the inertia. Guided by the
application to Saturn, we model a sandwiched stable stratified layer (SSL)
surrounded by two convective zones. A comprehensive analysis of the damping
behavior of convective flows at the edges of the SSL showed that the mean
penetration depth is controlled by the ratio of stratified and unstratified
buoyancy gradients and is hence independent of rotation. A scaling law is
derived and suggests that the penetration depth decreases with the square root
of the ratio of unstabilizing and stabilizing entropy gradients. The influence
of the Coriolis force, however, is evident by a modulation of the penetration
depth along latitude, since convective columns are elongated vertically and
hence pierce predominantly into the SSL around mid-latitudes and outside the
tangent cylinder. Our result also show that the penetration depth decreases
linearly with the flow length scale (low pass filter), confirming predictions
from the linear theory of rotating partially stratified convection
Scaling regimes in spherical shell rotating convection
Rayleigh-B\'enard convection in rotating spherical shells can be considered
as a simplified analogue of many astrophysical and geophysical fluid flows.
Here, we use three-dimensional direct numerical simulations to study this
physical process. We construct a dataset of more than 200 numerical models that
cover a broad parameter range with Ekman numbers spanning , Rayleigh numbers within the range and a Prandtl number unity. We investigate the scaling behaviours of
both local (length scales, boundary layers) and global (Nusselt and Reynolds
numbers) properties across various physical regimes from onset of rotating
convection to weakly-rotating convection. Close to critical, the convective
flow is dominated by a triple force balance between viscosity, Coriolis force
and buoyancy. For larger supercriticalities, a subset of our numerical data
approaches the asymptotic diffusivity-free scaling of rotating convection
in a narrow fraction of the parameter space delimited by
. Using a decomposition of the viscous
dissipation rate into bulk and boundary layer contributions, we establish a
theoretical scaling of the flow velocity that accurately describes the
numerical data. In rapidly-rotating turbulent convection, the fluid bulk is
controlled by a triple force balance between Coriolis, inertia and buoyancy,
while the remaining fraction of the dissipation can be attributed to the
viscous friction in the Ekman layers. Beyond , the
rotational constraint on the convective flow is gradually lost and the flow
properties vary to match the regime changes between rotation-dominated and
non-rotating convection. The quantity provides an accurate
transition parameter to separate rotating and non-rotating convection.Comment: 42 pages, 20 figures, 3 tables, accepted for publication in JF
Reversal and amplification of zonal flows by boundary enforced thermal wind
Zonal flows in rapidly-rotating celestial objects such as the Sun, gas or ice
giants form in a variety of surface patterns and amplitudes. Whereas the
differential rotation on the Sun, Jupiter and Saturn features a super-rotating
equatorial region, the ice giants, Neptune and Uranus harbour an equatorial jet
slower than the planetary rotation. Global numerical models covering the
optically thick, deep-reaching and rapidly rotating convective envelopes of gas
giants reproduce successfully the prograde jet at the equator. In such models,
convective columns shaped by the dominant Coriolis force typically exhibit a
consistent prograde tilt. Hence angular momentum is pumped away from the
rotation axis via Reynolds stresses. Those models are found to be strongly
geostrophic, hence a modulation of the zonal flow structure along the axis of
rotation, e.g. introduced by persistent latitudinal temperature gradients,
seems of minor importance. Within our study we stimulate these thermal
gradients and the resulting ageostrophic flows by applying an axisymmetric and
equatorially symmetric outer boundary heat flux anomaly () with
variable amplitude and sign. Such a forcing pattern mimics the thermal effect
of intense solar or stellar irradiation. Our results suggest that the
ageostrophic flows are linearly amplified with the forcing amplitude
leading to a more pronounced dimple of the equatorial jet (alike Jupiter). The
geostrophic flow contributions, however, are suppressed for weak , but
inverted and re-amplified once exceeds a critical value. The inverse
geostrophic differential rotation is consistently maintained by now also
inversely tilted columns and reminiscent of zonal flow profiles observed for
the ice giants. Analysis of the main force balance and parameter studies
further foster these results
Zonal flow scaling in rapidly-rotating compressible convection
The surface winds of Jupiter and Saturn are primarily zonal. Each planet
exhibits strong prograde equatorial flow flanked by multiple alternating zonal
winds at higher latitudes. The depth to which these flows penetrate has long
been debated and is still an unsolved problem. Previous rotating convection
models that obtained multiple high latitude zonal jets comparable to those on
the giant planets assumed an incompressible (Boussinesq) fluid, which is
unrealistic for gas giant planets. Later models of compressible rotating
convection obtained only few high latitude jets which were not amenable to
scaling analysis.
Here we present 3-D numerical simulations of compressible convection in
rapidly-rotating spherical shells. To explore the formation and scaling of
high-latitude zonal jets, we consider models with a strong radial density
variation and a range of Ekman numbers, while maintaining a zonal flow Rossby
number characteristic of Saturn.
All of our simulations show a strong prograde equatorial jet outside the
tangent cylinder. At low Ekman numbers several alternating jets form in each
hemisphere inside the tangent cylinder. To analyse jet scaling of our numerical
models and of Jupiter and Saturn, we extend Rhines scaling based on a
topographic -parameter, which was previously applied to an
incompressible fluid in a spherical shell, to compressible fluids. The
jet-widths predicted by this modified Rhines length are found to be in
relatively good agreement with our numerical model results and with cloud
tracking observations of Jupiter and Saturn.Comment: 17 pages, 12 figures, 3 tables, accepted for publication in PEP
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
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
Effects of a radially varying electrical conductivity on 3D numerical dynamos
The transition from liquid metal to silicate rock in the cores of the
terrestrial planets is likely to be accompanied by a gradient in the
composition of the outer core liquid. The electrical conductivity of a volatile
enriched liquid alloy can be substantially lower than a light-element-depleted
fluid found close to the inner core boundary. In this paper, we investigate the
effect of radially variable electrical conductivity on planetary dynamo action
using an electrical conductivity that decreases exponentially as a function of
radius. We find that numerical solutions with continuous, radially outward
decreasing electrical conductivity profiles result in strongly modified flow
and magnetic field dynamics, compared to solutions with homogeneous electrical
conductivity. The force balances at the top of the simulated fluid determine
the overall character of the flow. The relationship between Coriolis and
Lorentz forces near the outer boundary controls the flow and magnetic field
intensity and morphology of the system. Our results imply that a low
conductivity layer near the top of Mercury's liquid outer core is consistent
with its weak magnetic field.Comment: 30 pages, 11 figures, 2 tables. To be published in Physics of Earth
and Planetary Interiors (PEPI)
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