296 research outputs found
Double-diffusive erosion of the core of Jupiter
We present Direct Numerical Simulations of the transport of heat and heavy
elements across a double-diffusive interface or a double-diffusive staircase,
in conditions that are close to those one may expect to find near the boundary
between the heavy-element rich core and the hydrogen-helium envelope of giant
planets such as Jupiter. We find that the non-dimensional ratio of the buoyancy
flux associated with heavy element transport to the buoyancy flux associated
with heat transport lies roughly between 0.5 and 1, which is much larger than
previous estimates derived by analogy with geophysical double-diffusive
convection. Using these results in combination with a core-erosion model
proposed by Guillot et al. (2004), we find that the entire core of Jupiter
would be eroded within less than 1Myr assuming that the core-envelope boundary
is composed of a single interface. We also propose an alternative model that is
more appropriate in the presence of a well-established double-diffusive
staircase, and find that in this limit a large fraction of the core could be
preserved. These findings are interesting in the context of Juno's recent
results, but call for further modeling efforts to better understand the process
of core erosion from first principles.Comment: Accepted for publication in Ap
The Sun's meridional circulation and interior magnetic field
To date, no self-consistent numerical simulation of the solar interior has
succeeded in reproducing the observed thinness of the solar tachocline, and the
persistence of uniform rotation beneath it. Although it is known that the
uniform rotation can be explained by the presence of a global-scale confined
magnetic field, numerical simulations have thus far failed to produce any
solution where such a field remains confined against outward diffusion. We
argue that the problem lies in the choice of parameters for which these
numerical simulations have been performed. We construct a simple analytical
magneto-hydrodynamic model of the solar interior and identify several distinct
parameter regimes. For realistic solar parameter values, our results are in
broad agreement with the tachocline model of Gough & McIntyre. In this regime,
meridional flows driven at the base of the convection zone are of sufficient
amplitude to hold back the interior magnetic field against diffusion. For the
parameter values used in existing numerical simulations, on the other hand, we
find that meridional flows are significantly weaker and, we argue, unable to
confine the interior field. We propose a method for selecting parameter values
in future numerical models.Comment: 49 pages, 11 figures, in press in the Astrophysical Journa
A practical model of convective dynamics for stellar evolution calculations
Turbulent motions in the interior of a star play an important role in its
evolution, since they transport chemical species, thermal energy and angular
momentum. Our overall goal is to construct a practical turbulent closure model
for convective transport that can be used in a multi-dimensional stellar
evolution calculation including the effects of rotation, shear and magnetic
fields. Here, we focus on the first step of this task: capturing the well-known
transition from radiative heat transport to turbulent convection with and
without rotation, as well as the asymptotic relationship between turbulent and
radiative transport in the limit of large Rayleigh number. We extend the
closure model developed by Ogilvie (2003) and Garaud and Ogilvie (2005) to
include heat transport and compare it with experimental results of
Rayleigh-Benard convection.Comment: Conference proceeding for poster at conference "Unsolved problems in
Stellar Physics
Global shallow water magnetohydrodynamic waves in the solar tachocline
We derive analytical solutions and dispersion relations of global magnetic
Poincar\'e (magneto-gravity) and magnetic Rossby waves in the approximation of
shallow water magnetohydrodynamics. The solutions are obtained in a rotating
spherical coordinate system for strongly and weakly stable stratification
separately in the presence of toroidal magnetic field. In both cases magnetic
Rossby waves split into fast and slow magnetic Rossby modes. In the case of
strongly stable stratification (valid in the radiative part of the tachocline)
all waves are slightly affected by the layer thickness and the toroidal
magnetic field, while in the case of weakly stable stratification (valid in the
upper overshoot layer of the tachocline) magnetic Poincar\'e and fast magnetic
Rossby waves are found to be concentrated near the solar equator, leading to
equatorially trapped waves. However, slow magnetic Rossby waves tend to
concentrate near the poles, leading to polar trapped waves. The frequencies of
all waves are smaller in the upper weakly stable stratification region than in
the lower strongly stable stratification one
Individual and collective behavior of dust particles in a protoplanetary nebula
We study the interaction between gas and dust particles in a protoplanetary
disk, comparing analytical and numerical results. We first calculate
analytically the trajectories of individual particles undergoing gas drag in
the disk, in the asymptotic cases of very small particles (Epstein regime) and
very large particles (Stokes regime). Using a Boltzmann averaging method, we
then infer their collective behavior. We compare the results of this analytical
formulation against numerical computations of a large number of particles.
Using successive moments of the Boltzmann equation, we derive the equivalent
fluid equations for the average motion of the particles; these are
intrinsically different in the Epstein and Stokes regimes. We are also able to
study analytically the temporal evolution of a collection of particles with a
given initial size-distribution provided collisions are ignored.Comment: 15 pages, 9 figures, submitted to Ap
Dynamics of the solar tachocline II: the stratified case
We present a detailed numerical study of the Gough & McIntyre model for the
solar tachocline. This model explains the uniformity of the rotation profile
observed in the bulk of the radiative zone by the presence of a large-scale
primordial magnetic field confined below the tachocline by flows originating
from within the convection zone. We attribute the failure of previous numerical
attempts at reproducing even qualitatively Gough & McIntyre's idea to the use
of boundary conditions which inappropriately model the radiative--convective
interface. We emphasize the key role of flows downwelling from the convection
zone in confining the assumed internal field. We carefully select the range of
parameters used in the simulations to guarantee a faithful representation of
the hierarchy of expected lengthscales. We then present, for the first time, a
fully nonlinear and self-consistent numerical solution of the Gough & McIntyre
model which qualitatively satisfies the following set of observational
constraints: (i) the quenching of the large-scale differential rotation below
the tachocline - including in the polar regions - as seen by helioseismology
(ii) the confinement of the large-scale meridional flows to the uppermost
layers of the radiative zone as required by observed light element abundances
and suggested by helioseismic sound-speed data.Comment: 21 pages, 15 figures, submitted to MNRA
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