Research: Buoyant Bubbles
Flows involving the rise of buoyant bubbles have long been well understood
when &madash; as with air bubbles in water — viscosity or surface tension
can play an important role in regularizing the problem and stabilizing the
interface. However, there are real systems where such diffusivities or
tensions are so vanishingly small that they can play no role on any length
scale of interest. In these systems, often some other physical effect
rises to the occasion and acts to provide the necessary stabilization of
the interface; but then the resulting dynamics are quite different from
the more familiar cases. I have been working in particular on the
cases of a rising bubble in a magnetized medium, and a buoyant reactive
[ Magnetic Draping of Bubbles |
Propagation of Flame Bubbles |
Magnetic Draping of Galaxy Cluster Bubbles
Recent observations of galaxy cluster cooling
flows have revealed X-ray emission voids up to twice the size of our
own galaxy in size that have been identified with buoyant, magnetized
bubbles, presumably inflated by the central Active Galactic Nucleus
(AGN) of the cluster. These hot bubbles potentially help explain an
important mystery in understanding the Inter-Cluster Medium (ICM) by
providing a heat source; however, the mechanism by which the hot bubble
heats the surrounding medium remains unclear. Complicating the issue of
bubble/ICM interaction is that the interface is still poorly understood;
it is known that the interface remains quite sharp, and it's not clear
why that would be.
A projectile in a magnetized medium `draping' the field over itself, modifying
its later dynamics. From Dursi & Pfrommer (2007).
Recent numerical and linear stability theory work of mine, however,
Dursi & Pfrommer 2007)
has shown that for the case of a small
overdense core merging into a magnetized medium — even one quite weakly
magnetized,as one might expect in this context — the projectile `plows
up' field lines, building magnetic field strength up to dynamically
important and even dominant levels, as shown in the figure above.
This magnetic layer can have significant dynamic effects, from partly
stabilizing against instabilities (as shown in the linear theory work)
to more surprising effects including acting to decelerate the projectile.
These dynamical effects may be quite important, as
earlier work of mine done while supervising undergraduate
research student K. Robinson at Chicago (Robinson,
Dursi, et al. (2004)) showed that such a coherent magnetic
showed that such a coherent magnetic field
may be necessary for the maintenance of these bubbles, as absent any
such features, a hydrodynamic bubble will shred itself into at best a
`smoke ring' in one buoyant rise time (eg, the figure below),
making it very difficult to see how purely hydrodynamic flow could
explain both AGN heating and the persistence of such bubbles.
We now largely understand this behaviour for an over-dense core;
however, there in principle could be significant differences for an
under-dense bubble which is prone to breaking up. There there is some
evidence that they are similar, and our analysis has
confirmed that the timescales could well be sort enough for the draping
to successfully provide a protective `bubble wrap' for these objects,
as well. Further, there is the intriguing possibility that these
magnetized layers may be directly observable. I plan to continue this
work to examine these two questions, and apply this effect of `magnetic
draping' to other systems.
The work considered above includes only ideal magnetohydrodynamics
(MHD), and it is inferred that, because of the magnetic field geometry,
thermal conductivity across the drape will be strongly suppressed,
maintaining the sharpness of the interface. However, confirming this
requires self-consistent inclusion of the relevant thermal and magnetic
diffusivities — which in this context are themselves open research
topics. But therein lies opportunity; coupled with the possibility
of the direct observation of these drapes, one may be able to constrain
what the diffusivities must look like, and therefore contribute to the
understanding of another problem.
Propagation of Flame Bubbles
Another situation in which some other effect provides a stabilization of
a buoyant bubble is the case of a rising reactive bubble, or a `flame
bubble' (eg, the figure to the right). There are a number of
situations such studies relate to; an important system is Supernovae of
Type Ia, which are extremely interesting objects in their own right,
but are also used in measuring global parameters of the Universe (the
discovery that the Universe is accelerating its expansion, and thus the
inference of the existence of a `dark energy', is largely based on the
unexplained apparent uniformity of these objects).
However, increasing scrutiny shows Type Ia aren't as uniform as
previously thought; what's more, new observations suggest that there
may be populations of Type Ia which are very difficult to produce in the
standard picture. Understanding these events requires
a more detailed understanding of the ignition and early burning.
The burning in this situation is likely to ignite at points, meaning
that the initial behaviour is that of a rising flame bubble.
My earlier work has largely focused on planar (thermonuclear) burning
waves in this regime, both supersonic detonations
(Dursi & Timmes (2006),
Timmes et al. (2000))
and subsonic deflagrations or `flames' ,
Dursi et al. (2003))
including the instabilities of these propagating burning fronts and
their interaction with turbulence (see, eg, the figure to the left).
They are similar enough to the more familiar terrestrial equivalents
to be able to bring over much of the well-developed theory from the
combustion literature, but different enough to be extremely interesting,
and fundamental questions remain unanswered. My work on these flows
themselves are discussed in a later section.
With M. Zingale (SUNY SB), in collaboration with researchers at Lawrence
Berkeley National Laboratory, I have used a novel computational method
along with analytic arguments to examine the balance of flame propagation,
flame instabilities, and buoyancy the early behaviour of flame bubbles in
Type Ia supernovae
(Zingale & Dursi 2007).
The analytics are essential
to understand the dynamics of the situation, and the simulations are
extremely large-scale computations, due to the large range of scales
between the flame thickness and the hydrodynamic scales. We have
considered such questions as when the centre of the star is consumed by
the first flames; we have also shown the tendency of a rising flame bubble
to fragment (assisted by my earlier work in non-reactive bubbles),
and calculated a characteristic fragmentation scale. This fragmentation
scale drops precipitously as degeneracy lifts in the star, providing a
rapid cascade of fragmentation — and thus an increase in burning area
— at just the time that an increase in burning rate is needed to match
observations. This novel burning model will be examined in future work.
My work so far, then, examines ignition in one-zone (0d) (eg,
Dursi & Timmes (2006))
models and early stages of burning in 2d and 3d.
My next goal is to extend the work in both directions to build a model
which goes from ignition points to early burning phases. This area is
currently the biggest unanswered question in Type Ia supernovae models;
while the technology has developed to do very sophisticated large-scale
simulations of the explosions given some set of initial large-scale
burning, they must be initialized with some guess as to what that burning
looks like. The goal of my current work is to give a prescription
for what that large-scale burning should look like given some progenitor
model and the convective turbulence expected from the long-term simmering.
Results from a simulation of spherically compressed reactive turbulence.
To do this will require extending the consideration of ignition from
one-zone models to 1d and higher; this brings in a great deal more
physics, and while estimates can be done analytically, precision in the
ignition conditions will require very large parameter studies (but of very
modest individual computations) to demarcate the `flammability conditions'
for given hotspots. From there, it will be necessary to extend the
early burning work done already to include in a more sophisticated way
the effects of turbulence and instabilities; the result of these two
efforts will be a significant step towards a `soup-to-nuts' model of
the ignition and early burning stages of Type Ia supernovae, which would
apply in many different scenarios beyond the standard model, such
as models where the initial reactive turbulence is highly compressed
(as in the figure to the right.)
L. J. Dursi, C. Pfrommer.
Draping of Cluster Magnetic Fields over Bullets and Bubbles -- Morphology and Dynamic Effects,
arXiv:0711.0213, ApJ submitted, 2007. (3D renderings can be investigated in this manuscript if Adobe Acrobat Reader 8.01 or better is used)
M. Zingale, L. J. Dursi.
Propagation of the First Flames in Type Ia Supernovae,
ApJ, 656:333-346, 2007.
L. J. Dursi. The Linear Stability of Astrophysical Flames in Magnetic Fields,
ApJ, 606:1039-1056, May 2004.
L. J. Dursi, F. X. Timmes.
Local Ignition in Carbon/Oxygen White Dwarfs -- I: One-zone Ignition and Spherical Shock Ignition of Detonations.
ApJ, 641:1071, Apr 2006.
K. Robinson, L. J. Dursi, P. M. Ricker, R. Rosner, A. C. Calder,
M. Zingale, J. W. Truran, T. Linde, A. Caceres, B. Fryxell, ,
K. Olson, K. Riley, A. Siegel, and N. Vladimirova.
Morphology of Rising Hydrodynamic and Magnetohydrodynamic Bubbles from Numerical Simulations.
ApJ , 601(2):621-643, February 2004.
L. J. Dursi, M. Zingale, A. C. Calder, B. Fryxell, F. X. T. Timmes,
N. Vladimirova, R. Rosner, A. Caceres, D. Q. Lamb, K. Olson, P. M.
Ricker, K. Riley, A. Siegel, and J. W. Truran.
The Response of Model and Astrophysical Thermonuclear Flames to Curvature and Stretch.
ApJ , 595(2):955-979, October 2003.
F. X. Timmes, M. Zingale, K. Olson, B. Fryxell, P. Ricker, A. C.
Calder, L. J. Dursi, H. Tufo, P. MacNeice, J. W. Truran, and
On the Cellular Structure of Carbon Detonations.
ApJ , 543:938-954, November 2000.
M. Zingale, L. J. Dursi, J. ZuHone, A. C. Calder, B. Fryxell,
T. Plewa, J. W. Truran, A. Caceres, K. Olson, P. Ricker,
K. Riley, R. Rosner, A. Siegel, F. X. Timmes, and N. Vladimirova.
Mapping Initial Hydrostatic Models in Godunov Codes.
ApJSS , 143(2):539-566, December 2002.
Sweeping up a Magnetic Sheath: Magnetic Draping over Moving Cores and Bubbles in Galaxy Clusters
Accretion and Explosion: the Astrophysics of Degenerate Stars, KITP, May 17 2007
A talk given while I was in residence at the KITP program
on supernovae in May 2007.
The talk is on work examining `magnetic draping' in galaxy clusters.
Video or audio of the talk, as well as the slides, are available
at the KITP website.
First Flames: Burning, Turbulence, and Buoyancy
Paths to Exploding Stars: Accretion and Eruption, KITP, Mar 2007
An invited talk to the KITP conference during the
program Accretion and Explosion: the Astrophysics of Degenerate Stars
at KITP. The talk discusses
the ignition and earliest burning phases (eg, burning bubbles) in a Type Ia supernovae.
(Choppy) video or audio of the talk, as well as the slides, is available
at the conference webpage.
Simulating Astrophysical Combustion with the FLASH code
CAIMS/MITACS Joint Annual Conference, June 2006
An invited talk to the Scientific
Computing session of the annual Canadian applied mathematics
conference discussing simulating combustion in an astrophysical context,
and the computational choices that this regime suggests.
Local Ignition in Carbon-Oxygen White Dwarfs: One Zone Ignition, and Spherical Shock Ignition of Detonations
208th AAS meeting, June 2006
A presentation describing recent work on the physics of local ignition in Type Ia supernovae.
Towards Understanding some Astrophysical Flows using Multiscale Approaches with the FLASH code
HPCS 2006, May 2006
A discussion of some of our attempts to simulate turbulent astrophysical flows
with interesting physics on disparate scales using simple multiscale approaches.
Grungy Gastrophysics and Cosmology
class="bold" href="http://www.ap.stmarys.ca/">St. Mary's University, Nov 2005
This discusses the Type Ia supernovae problem,
the very detailed interplay of physics needed to really understand
how they blow up, and arguing that the problem is really still very
Buoyancy and Astrophysics
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Toronto Astrophysical Gas Dynamics Seminar, Oct 2004
[PDF] [OpenOffice .sxi]
Rayleigh-Taylor, RT-plus burning, and rising bubbles; an overview of some astrophysical
problems involving buoyancy and why such simple problems are so surprisingly difficult
to deal with.