171 research outputs found
A note on transition, turbulent length scales and transport in differentially rotating flows
In this note we address the issue of hydrodynamical instabilities in
Astrophysical rotating shear flows in the light of recent publications focused
on the possibility for differential rotation to trigger and sustain turbulence
in the absence of a magnetic field. We wish to present in a synthetic form the
major arguments in favor of this thesis along with a simple schematic scenario
of the transition to and self-sustenance of such turbulence. We also propose
that the turbulent diffusion length scale scales as the local Rossby number of
the mean flow. A new prescription for the turbulent viscosity is introduced.
This viscosity reduces to the so-called beta-prescription in the case of
velocity profiles with a constant Rossby number, which includes Keplerian
rotating flows.Comment: 4 pages, accepted for publication in "Astronomy and Astrophysics
Lunar and planetary studies
This grant supports the core program in planetary astronomy at Caltech. The research includes observations in the IR, sub-mm, mm and cm wavelengths at national and Caltech observatories with a strong emphasis on integrating the observations with spacecraft data and with models of atmospheric structure, dynamics and chemistry. Muhleman's group made extensive observations of Saturn, Uranus and Neptune which are being interpreted in terms of deep atmospheric structures which are obvious in the 2 and 6 cm maps of Saturn and Uranus. The microwave measurements are one of the few sources of information below the 2 bar level. Goldreich is investigating the dynamics of narrow rings with postdoctoral fellow, Pierre-Yves Longaretti. Their work has focused on the role of collisional stresses on the precession of the rings, since the Voyager radio science results imply that the previous model based on the ring's self-gravity is not the entire story. In addition Borderies, Goldreich and Tremaine have completed an investigation of the dynamics of the Encke division in Saturn's A ring
Gravitational instability of slowly rotating isothermal spheres
We discuss the statistical mechanics of rotating self-gravitating systems by
allowing properly for the conservation of angular momentum. We study
analytically the case of slowly rotating isothermal spheres by expanding the
solutions of the Boltzmann-Poisson equation in a series of Legendre
polynomials, adapting the procedure introduced by Chandrasekhar (1933) for
distorted polytropes. We show how the classical spiral of Lynden-Bell & Wood
(1967) in the temperature-energy plane is deformed by rotation. We find that
gravitational instability occurs sooner in the microcanonical ensemble and
later in the canonical ensemble. According to standard turning point arguments,
the onset of the collapse coincides with the minimum energy or minimum
temperature state in the series of equilibria. Interestingly, it happens to be
close to the point of maximum flattening. We determine analytically the
generalization of the singular isothermal solution to the case of a slowly
rotating configuration. We also consider slowly rotating configurations of the
self-gravitating Fermi gas at non zero temperature.Comment: Submitted to A&
On the Magnetic Prandtl Number Behavior of Accretion Disks
We investigate the behavior of the magnetic Prandtl number (ratio of
microscopic viscosity to resistivity) for accretion sources. Generally this
number is very small in standard accretion disk models, but can become larger
than unity within Schwarzschild radii of the central mass. Recent
numerical investigations suggest a marked dependence of the level of MHD
turbulence on the value of the Prandtl number. Hence, black hole and neutron
star accretors, i.e. compact X-ray sources, are affected. The astrophysical
consequences of this could be significant, including a possible route to
understanding the mysterious state changes that have long characterized these
sources.Comment: 15 pages, 6 figures. Accepted for publication in the Astrophysical
Journal (February 10, 2008 issue.) Minor changes from original submissio
Pressure-driven instabilities in astrophysical jets
Astrophysical jets are widely believed to be self-collimated by the
hoop-stress due to the azimuthal component of their magnetic field. However
this implies that the magnetic field is largely dominated by its azimuthal
component in the outer jet region. In the fusion context, it is well-known that
such configurations are highly unstable in static columns, leading to plasma
disruption. It has long been pointed out that a similar outcome may follow for
MHD jets, and the reasons preventing disruption are still not elucidated,
although some progress has been accomplished in the recent years.
In these notes, I review the present status of this open problem for
pressure-driven instabilities, one of the two major sources of ideal MHD
instability in static columns (the other one being current-driven
instabilities).
I first discuss in a heuristic way the origin of these instabilities.
Magnetic resonances and magnetic shear are introduced, and their role in
pressure-driven instabilities discussed in relation to Suydam's criterion. A
dispersion relation is derived for pressure-driven modes in the limit of large
azimuthal magnetic fields, which gives back the two criteria derived by
Kadomtsev for this instability. The growth rates of these instabilities are
expected to be short in comparison with the jet propagation time.
What is known about the potential stabilizing role of the axial velocity of
jets is then reviewed. In particular, a nonlinear stabilization mechanism
recently identified in the fusion literature is discussed.
Key words: Ideal MHD: stability, pressure-driven modes; Jets: stabilityComment: 20 pages, 3 figures. Lecture given at the JETSET European school
"Numerical MHD and Instabilities". To be published by Springer in the
"Lectures notes in physics" serie
Connections Between Local and Global Turbulence in Accretion Disks
We analyze a suite of global magnetohydrodynamic (MHD) accretion disk
simulations in order to determine whether scaling laws for turbulence driven by
the magnetorotational instability, discovered via local shearing box studies,
are globally robust. The simulations model geometrically-thin disks with zero
net magnetic flux and no explicit resistivity or viscosity. We show that the
local Maxwell stress is correlated with the self-generated local vertical
magnetic field in a manner that is similar to that found in local simulations.
Moreover, local patches of vertical field are strong enough to stimulate and
control the strength of angular momentum transport across much of the disk. We
demonstrate the importance of magnetic linkages (through the low-density
corona) between different regions of the disk in determining the local field,
and suggest a new convergence requirement for global simulations -- the
vertical extent of the corona must be fully captured and resolved. Finally, we
examine the temporal convergence of the average stress, and show that an
initial long-term secular drift in the local flux-stress relation dies away on
a time scale that is consistent with turbulent mixing of the initial magnetic
field.Comment: 8 Pages, 7 Figures ApJ, In Pres
Perceptions and experiences of belonging during the transition from primary to secondary school
A young person’s sense of belonging at school can affect their level of motivation, academic achievement and wellbeing. During the transition from primary to secondary school, one’s sense of belonging may be affected by the changes and challenges encountered.
This paper reports some of the findings from a larger qualitative longitudinal study that investigated the factors that contribute to educational resilience during the transition from primary to secondary school. Data gathered from interviews with sixteen Year 6 students from three Victorian primary schools over a period of eighteen months is presented and analysed.
A key theme identified from the larger study was belonging. This paper specifically reports on how belonging is perceived and experienced by students during the transition to secondary school. Understanding sense of belonging from young people’s views, may help inform and effectively shape practices relevant to policy, pedagogy and teacher training. Implications for practice are discussed
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