571 research outputs found
A test of time-dependent theories of stellar convection
Context: In Cepheids close to the red edge of the classical instability
strip, a coupling occurs between the acoustic oscillations and the convective
motions close to the surface.The best topical models that account for this
coupling rely on 1-D time-dependent convection (TDC) formulations. However,
their intrinsic weakness comes from the large number of unconstrained free
parameters entering in the description of turbulent convection. Aims: We
compare two widely used TDC models with the first two-dimensional nonlinear
direct numerical simulations (DNS) of the convection-pulsation coupling in
which the acoustic oscillations are self-sustained by the kappa-mechanism.
Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC
recipes are constrained using a chi2-test with the time-dependent convective
flux that evolves in nonlinear simulations of highly-compressible convection
with kappa-mechanism. Results: This work emphasises some inherent limits of TDC
models, that is, the temporal variability and non-universality of their free
parameters. More importantly, within these limits, Stellingwerf's formalism is
found to give better spatial and temporal agreements with the nonlinear
simulation than Kuhfuss's one. It may therefore be preferred in 1-D TDC
hydrocodes or stellar evolution codes.Comment: 7 pages, 5 figures, 2 tables, accepted for publication in A&
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
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
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
Scaling laws in spherical shell dynamos with free-slip boundaries
Numerical simulations of convection driven rotating spherical shell dynamos
have often been performed with rigid boundary conditions, as is appropriate for
the metallic cores of terrestrial planets. Free-slip boundaries are more
appropriate for dynamos in other astrophysical objects, such as gas-giants or
stars. Using a set of 57 direct numerical simulations, we investigate the
effect of free-slip boundary conditions on the scaling properties of heat flow,
flow velocity and magnetic field strength and compare it with earlier results
for rigid boundaries. We find that the nature of the mechanical boundary
condition has only a minor influence on the scaling laws. We also find that
although dipolar and multipolar dynamos exhibit approximately the same scaling
exponents, there is an offset in the scaling pre-factors for velocity and
magnetic field strength. We argue that the offset can be attributed to the
differences in the zonal flow contribution between dipolar and multipolar
dynamos.Comment: 10 pages, 9 figures, 1 table. To appear 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
Anelastic dynamo models with variable electrical conductivity: an application to gas giants
The observed surface dynamics of Jupiter and Saturn is dominated by a banded
system of zonal winds. Their depth remains unclear but they are thought to be
confined to the very outer envelopes where hydrogen remains molecular and the
electrical conductivity is small. The dynamo maintaining the dipole-dominated
magnetic fields of both gas giants likely operates in the deeper interior where
hydrogen assumes a metallic state. Here, we present numerical simulations that
attempt to model both the zonal winds and the interior dynamo action in an
integrated approach. Using the anelastic version of the MHD code MagIC, we
explore the effects of density stratification and radial electrical
conductivity variation. The electrical conductivity is mostly assumed to remain
constant in the thicker inner metallic region and it decays exponentially
towards the outer boundary throughout the molecular envelope. Our results show
that the combination of stronger density stratification and weaker conducting
outer layer is essential for reconciling dipole dominated dynamo action and a
fierce equatorial zonal jet. Previous simulations with homogeneous electrical
conductivity show that both are merely exclusive, with solutions either having
strong zonal winds and multipolar magnetic fields or weak zonal winds and
dipole-dominated magnetic fields. All jets tend to be geostrophic and therefore
reach right through the convective shell in our simulations. The particular
setup explored here allows a strong equatorial jet to remain confined to the
weaker conducting outer region where it does not interfere with the deeper
seated dynamo action. The flanking mid to high latitude jets, on the other
hand, have to remain faint to yield a strongly dipolar magnetic field. The
fiercer jets on Jupiter and Saturn only seem compatible with the observed
dipolar fields when they remain confined to a weaker conducting outer layer.Comment: 16 pages, 11 figures, 2 tables, submitted to PEP
- …