136 research outputs found
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
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&
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
Numerical simulations of the kappa-mechanism with convection
A strong coupling between convection and pulsations is known to play a major
role in the disappearance of unstable modes close to the red edge of the
classical Cepheid instability strip. As mean-field models of time-dependent
convection rely on weakly-constrained parameters, we tackle this problem by the
means of 2-D Direct Numerical Simulations (DNS) of kappa-mechanism with
convection.
Using a linear stability analysis, we first determine the physical conditions
favourable to the kappa-mechanism to occur inside a purely-radiative layer.
Both the instability strips and the nonlinear saturation of unstable modes are
then confirmed by the corresponding DNS. We next present the new simulations
with convection, where a convective zone and the driving region overlap. The
coupling between the convective motions and acoustic modes is then addressed by
using projections onto an acoustic subspace.Comment: 5 pages, 6 figures, accepted for publication in Astrophysics and
Space Science, HELAS workshop (Rome june 2009
From solar-like to anti-solar differential rotation in cool stars
Stellar differential rotation can be separated into two main regimes:
solar-like when the equator rotates faster than the poles and anti-solar when
the polar regions rotate faster than the equator. We investigate the transition
between these two regimes with 3-D numerical simulations of rotating spherical
shells. We conduct a systematic parameter study which also includes models from
different research groups. We find that the direction of the differential
rotation is governed by the contribution of the Coriolis force in the force
balance, independently of the model setup (presence of a magnetic field,
thickness of the convective layer, density stratification). Rapidly-rotating
cases with a small Rossby number yield solar-like differential rotation, while
weakly-rotating models sustain anti-solar differential rotation. Close to the
transition, the two kinds of differential rotation are two possible bistable
states. This study provides theoretical support for the existence of anti-solar
differential rotation in cool stars with large Rossby numbers.Comment: 5 pages, 6 figures, accepted for publication in MNRA
Explaining Jupiter's magnetic field and equatorial jet dynamics
Spacecraft data reveal a very Earth-like Jovian magnetic field. This is
surprising since numerical simulations have shown that the vastly different
interiors of terrestrial and gas planets can strongly affect the internal
dynamo process. Here we present the first numerical dynamo that manages to
match the structure and strength of the observed magnetic field by embracing
the newest models for Jupiter's interior. Simulated dynamo action primarily
occurs in the deep high electrical conductivity region while zonal flows are
dynamically constrained to a strong equatorial jet in the outer envelope of low
conductivity. Our model reproduces the structure and strength of the observed
global magnetic field and predicts that secondary dynamo action associated to
the equatorial jet produces banded magnetic features likely observable by the
Juno mission. Secular variation in our model scales to about 2000 nT per year
and should also be observable during the one year nominal mission duration.Comment: 7 pages, 4 figures, accepted for publication in Geophysical Research
Letter
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