826 research outputs found
On the dynamics of radiative zones in rotating stars
In this lecture I try to explain the basic dynamical processes at work in a
radiative zone of a rotating star. In particular, the notion of baroclinicity
is thoroughly discussed. Attention is specially directed to the case of
circulations and the key role of angular momentum conservation is stressed. The
specific part played by viscosity is also explained. The old approach of
Eddington and Sweet is reviewed and criticized in the light of the seminal
papers of Busse 1981 and Zahn 1992. Other examples taken in the recent
literature are also presented; finally, I summarize the important points.Comment: 21 pages 5 figure
Dynamics of the radiative envelope of rapidly rotating stars: Effects of spin-down driven by mass loss
(abridged) This paper aims at deciphering the dynamics of the envelope of a
rotating star when some angular momentum loss due to mass loss is present. We
especially wish to know when the spin-down flow forced by the mass loss
supersedes the baroclinic flows that pervade the radiative envelope of rotating
stars. We consider a Boussinesq fluid enclosed in a rigid sphere whose flows
are forced both by the baroclinic torque, the spin-down of an outer layer, and
an outward mass flux. The spin-down forcing is idealized in two ways: either by
a rigid layer that imposes its spinning down velocity at some interface or by a
turbulent layer that imposes a stress at this same interface to the interior of
the star. In the case where the layer is rigid and imposes its velocity, we
find that, as the mass-loss rate increases, the flow inside the star shows two
transitions: the meridional circulation associated with baroclinic flows is
first replaced by its spin-down counterpart, while at much stronger mass-loss
rates the baroclinic differential rotation is superseded by the spin-down
differential rotation. In fact, we find three wind regimes: weak (or no wind),
moderate, and strong. In the first case, the flow in the radiative envelope is
of baroclinic origin. In the moderate case, the circulation results from the
spin-down while the differential rotation may either be of baroclinic or of
spin-down origin, depending on the coupling between mass and angular momentum
losses. For fast rotating stars, our model says that the moderate wind regime
starts when mass loss is higher than ~1e-11 Msun/yr. In the strong wind case,
the flow in the radiative envelope is mainly driven by angular momentum
advection. This latter transition depends on the mass and the rotation rate of
the star, being around 1e-8 Msun/yr for a 3 Msun ZAMS star rotating at 200 km/s
according to our model.Comment: 13 pages, 9 figures, to appear in Astronomy and Astrophysic
Inertial waves in a differentially rotating spherical shell
We investigate the properties of small-amplitude inertial waves propagating
in a differentially rotating incompressible fluid contained in a spherical
shell. For cylindrical and shellular rotation profiles and in the inviscid
limit, inertial waves obey a second-order partial differential equation of
mixed type. Two kinds of inertial modes therefore exist, depending on whether
the hyperbolic domain where characteristics propagate covers the whole shell or
not. The occurrence of these two kinds of inertial modes is examined, and we
show that the range of frequencies at which inertial waves may propagate is
broader than with solid-body rotation. Using high-resolution calculations based
on a spectral method, we show that, as with solid-body rotation, singular modes
with thin shear layers following short-period attractors still exist with
differential rotation. They exist even in the case of a full sphere. In the
limit of vanishing viscosities, the width of the shear layers seems to weakly
depend on the global background shear, showing a scaling in E^{1/3} with the
Ekman number E, as in the solid-body rotation case. There also exist modes with
thin detached layers of width scaling with E^{1/2} as Ekman boundary layers.
The behavior of inertial waves with a corotation resonance within the shell is
also considered. For cylindrical rotation, waves get dramatically absorbed at
corotation. In contrast, for shellular rotation, waves may cross a critical
layer without visible absorption, and such modes can be unstable for small
enough Ekman numbers.Comment: 31 pages, 16 figures, accepted for publication in Journal of Fluid
Mechanic
The Sun's Supergranulation
Supergranulation is a fluid-dynamical phenomenon taking place in the solar
photosphere, primarily detected in the form of a vigorous cellular flow pattern
with a typical horizontal scale of approximately 30--35~megameters, a dynamical
evolution time of 24--48~h, a strong 300--400~m/s (rms) horizontal flow
component and a much weaker 20--30~m/s vertical component. Supergranulation was
discovered more than sixty years ago, however, explaining its physical origin
and most important observational characteristics has proven extremely
challenging ever since, as a result of the intrinsic multiscale, nonlinear
dynamical complexity of the problem concurring with strong observational and
computational limitations. Key progress on this problem is now taking place
with the advent of 21st-century supercomputing resources and the availability
of global observations of the dynamics of the solar surface with high spatial
and temporal resolutions. This article provides an exhaustive review of
observational, numerical and theoretical research on supergranulation, and
discusses the current status of our understanding of its origin and dynamics,
most importantly in terms of large-scale nonlinear thermal convection, in the
light of a selection of recent findings.Comment: Major update of 2010 Liv. Rev. Sol. Phys. review. Addresses many new
theoretical, numerical and observational developments. All sections,
including discussion, revised extensively. Also includes previously
unpublished results on nonlinear dynamics of convection in large domains, and
lagrangian transport at the solar surfac
More concerning the anelastic and subseismic approximations for low-frequency modes in stars
Two approximations, namely the subseismic approximation and the anelastic
approximation, are presently used to filter out the acoustic modes when
computing low frequency modes of a star (gravity modes or inertial modes). In a
precedent paper (Dintrans & Rieutord 2001), we observed that the anelastic
approximation gave eigenfrequencies much closer to the exact ones than the
subseismic approximation. Here, we try to clarify this behaviour and show that
it is due to the different physical approach taken by each approximation: On
the one hand, the subseismic approximation considers the low frequency part of
the spectrum of (say) gravity modes and turns out to be valid only in the
central region of a star; on the other hand, the anelastic approximation
considers the Brunt-Vaisala frequency as asymptotically small and makes no
assumption on the order of the modes. Both approximations fail to describe the
modes in the surface layers but eigenmodes issued from the anelastic
approximation are closer to those including acoustic effects than their
subseismic equivalent.
We conclude that, as far as stellar eigenvalue problems are concerned, the
anelastic approximation is better suited for simplifying the eigenvalue problem
when low-frequency modes of a star are considered, while the subseismic
approximation is a useful concept when analytic solutions of high order
low-frequency modes are needed in the central region of a star.Comment: 5 pages 3 fig, to appear in MNRA
Two-dimensional models of early-type fast rotating stars: new challenges in stellar physics
Two-dimensional models of rapidly rotating stars are already unavoidable for
the interpretation of interferometric or asteroseismic data of this kind of
stars. When combined with time evolution, they will allow the including of a
more accurate physics for the computation of element transport and the
determination of surface abundances. In addition, modeling the evolution of
rotation will improve gyrochronology.
Presently, two-dimensional ESTER models predict the structure and the
large-scale flows (differential rotation and meridional circulation) of stars
with mass larger than 1.7Msun at any rotation rate. Main sequence evolution can
be mimicked by varying the hydrogen content of the convective core. Models have
been successfully tested on half a dozen of nearby fast rotating stars observed
with optical or infra-red interferometers. They are now the right tool to
investigate the oscillation spectrum of early-type fast rotators.Comment: 10 pages, to appear in the proceedings of the conference "New
advances in stellar physics: from microscopic to macroscopic processes",
Roscoff, May 201
Completeness of Inertial Modes of an Incompressible Non-Viscous Fluid in a Corotating Ellipsoid
Inertial modes are the eigenmodes of contained rotating fluids restored by
the Coriolis force. When the fluid is incompressible, inviscid and contained in
a rigid container, these modes satisfy Poincar\'e's equation that has the
peculiarity of being hyperbolic with boundary conditions. Inertial modes are
therefore solutions of an ill-posed boundary-value problem. In this paper we
investigate the mathematical side of this problem. We first show that the
Poincar\'e problem can be formulated in the Hilbert space of square-integrable
functions, with no hypothesis on the continuity or the differentiability of
velocity fields. We observe that with this formulation, the Poincar\'e operator
is bounded and self-adjoint and as such, its spectrum is the union of the point
spectrum (the set of eigenvalues) and the continuous spectrum only. When the
fluid volume is an ellipsoid, we show that the inertial modes form a complete
base of polynomial velocity fields for the square-integrable velocity fields
defined over the ellipsoid and meeting the boundary conditions. If the
ellipsoid is axisymmetric then the base can be identified with the set of
Poincar\'e modes, first obtained by Bryan (1889), and completed with the
geostrophic modes.Comment: 19 pages, 1 figure, to appear in Physical Review
Tracking granules at the Sun's surface and reconstructing velocity fields. II. Error analysis
The determination of horizontal velocity fields at the solar surface is
crucial to understanding the dynamics and magnetism of the convection zone of
the sun. These measurements can be done by tracking granules.
Tracking granules from ground-based observations, however, suffers from the
Earth's atmospheric turbulence, which induces image distortion. The focus of
this paper is to evaluate the influence of this noise on the maps of velocity
fields.
We use the coherent structure tracking algorithm developed recently and apply
it to two independent series of images that contain the same solar signal.
We first show that a k-\omega filtering of the times series of images is
highly recommended as a pre-processing to decrease the noise, while, in
contrast, using destretching should be avoided. We also demonstrate that the
lifetime of granules has a strong influence on the error bars of velocities and
that a threshold on the lifetime should be imposed to minimize errors. Finally,
although solar flow patterns are easily recognizable and image quality is very
good, it turns out that a time sampling of two images every 21 s is not
frequent enough, since image distortion still pollutes velocity fields at a 30%
level on the 2500 km scale, i.e. the scale on which granules start to behave
like passive scalars.
The coherent structure tracking algorithm is a useful tool for noise control
on the measurement of surface horizontal solar velocity fields when at least
two independent series are available.Comment: in press in Astronomy and Astrophysics, 9 page
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