Natalia Vladimirova

Morphology of Rising Hydrodynamic and Magnetohydrodynamic Bubbles from Numerical Simulations

Recent Chandra and XMM-Newton observations of galaxy cluster cooling flows have revealed X-ray emission voids of up to 30 kpc in size that have been identified with buoyant, magnetized bubbles. Motivated by these observations, we have investigated the behavior of rising bubbles in stratified atmospheres using the FLASH adaptive-mesh simulation code. We present results from two-dimensional simulations with and without the effects of magnetic fields and with varying bubble sizes and background stratifications. We find purely hydrodynamic bubbles to be unstable; a dynamically important magnetic field is required to maintain a bubbles integrity. This suggests that, even absent thermal conduction, for bubbles to be persistent enough to be regularly observed, they must be supported in large part by magnetic fields. Thermal conduction unmitigated by magnetic fields can dissipate the bubbles even faster. We also observe that the bubbles leave a tail as they rise; the structure of these tails can indicate the history of the dynamics of the rising bubble.

Mapping Initial Hydrostatic Models in Godunov Codes

We look in detail at the process of mapping an astrophysical initial model from a stellar evolution code onto the computational grid of an explicit, Godunov-type code while maintaining hydrostatic equilibrium. This mapping process is common in astrophysical simulations, when it is necessary to follow short-timescale dynamics after a period of long-timescale buildup. We look at the effects of spatial resolution, boundary conditions, the treatment of the gravitational source terms in the hydrodynamics solver, and the initialization process itself. We conclude with a summary detailing the mapping process that yields the lowest ambient velocities in the mapped model.

Flame Evolution During Type Ia Supernovae and the Deflagration Phase in the Gravitationally Confined Detonation Scenario

We develop an improved method for tracking the nuclear flame during the deflagration phase of a Type Ia supernova and apply it in a study of the variation in outcomes expected from the gravitationally confined detonation (GCD) paradigm. A simplified three-stage burning model and a nonstatic ash state are integrated with an artificially thickened advection-diffusion-reaction (ADR) flame front in order to provide an accurate but highly efficient representation of the energy release and electron capture in and after the unresolvable flame. We demonstrate that neither our ADR nor our energy release methods generate significant acoustic noise, as has been a problem with previous ADR-based schemes. We proceed to model aspects of the deflagration, particularly the role of buoyancy of the hot ash, and find that our methods are reasonably well behaved with respect to numerical resolution. We show that if a detonation occurs in material swept up by the material ejected by the first rising bubble but gravitationally confined to the white dwarf (WD) surface (the GCD paradigm), the density structure of the WD at detonation is systematically correlated with the distance of the deflagration ignition point from the center of the star. Coupled to a suitably stochastic ignition process, this correlation may provide a plausible explanation for the variety of nickel masses seen in Type Ia supernovae.

Capturing the Fire: Flame Energetics and Neutronization for Type Ia Supernova Simulations

We develop and calibrate a realistic model flame for hydrodynamic simulations of deflagrations in white dwarf (Type Ia) supernovae. Our flame model builds on the advection-diffusion-reaction model of Khokhlov and includes electron screening and Coulomb corrections to the equation of state in a self-consistent way. We calibrate this model flame—its energetics and timescales for energy release and neutronization—with self-heating reaction network calculations that include both these Coulomb effects and up-to-date weak interactions. The burned material evolves postflame due to both weak interactions and hydrodynamic changes in density and temperature. We develop a scheme to follow the evolution, including neutronization, of the NSE state subsequent to the passage of the flame front. As a result, our model flame is suitable for deflagration simulations over a wide range of initial central densities and can track the temperature and electron fraction of the burned material through the explosion and into the expansion of the ejecta.

Flame enhancement and quenching in fluid flows

We perform direct numerical simulations of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on the reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies ν ∼ aU + b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain ν ∼ U 1/4. We also study the flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of size W can be typically quenched by a flow with amplitude U ∼ αW. The constant α depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ∼ W 4 if the cell size is smaller than a critical value.

Two-dimensional model of phase segregation in liquid binary mixtures with an initial concentration gradient

We simulate the phase segregation of a deeply quenched binary mixture with an initial concentration gradient. Our theoretical model follows the standard model H, where convection and di!usion are coupled via a body force, expressing the tendency of the demixing system to minimize its free energy. This driving force induces a material #ux much larger than that due to pure molecular di!usion, as in a typical case the Peclet number a, expressing here the ratio of thermal to viscous forces, is of the order of 105. Integrating the equations of motion in 2D, we show that the behavior of the system depends on the values of the Peclet number a and the non-dimensional initial concentration gradient c. In particular, the morphology of the system during the separation process re#ects the competition between the capillarity-induced drop migration along the concentration gradient and the random#uctuations generated by the interactions of the drops with the local environment. For large a, the nucleating drops grow with time, until they reach a maximum size, whose value decreases as the Peclet number and the initial concentration gradient increase. This behavior is due to the fact that the nucleating drops do not have the chance to grow further, as they tend to move towards the homogeneous regions where they are assimilated. ( 2000 Published by Elsevier Science Ltd. All rights reserved.

Self-Similarity and Universality in Rayleigh-Taylor, Boussinesq Turbulence

We report and discuss case study simulations of the Rayleigh–Taylor instability in the Boussinesq, incompressible regime developed to turbulence. Our main focus is on a statistical analysis of density and velocity fluctuations inside of the already developed and growing in size mixing zone. Novel observations reported in the article concern self-similarity of the velocity and density fluctuations spectra inside of the mixing zone snapshot, independence of the spectra of the horizontal slice level, and universality showing itself in a virtual independence of the internal structure of the mixing zone, measured in the rescaled spatial units, of the initial interface perturbations.

Model flames in the Boussinesq limit: The effects of feedback

We have studied the fully nonlinear behavior of premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. The key results include the establishment of criteria for when such flames propagate as simple planar flames, elucidation of scaling laws for the effective flame speed, and a study of the stability properties of these flames. The simplicity of some of our scaling results suggests that analytical work may further advance our understandings of buoyant flames.

Flame capturing with an advection–reaction–diffusion model

We conduct several verification tests of the advection–reaction–diffusion flame-capturing model, developed by Khokhlov in 1995 for subsonic nuclear burning fronts in supernova simulations. We find that energy conservation is satisfied, but there is systematic error in the computed flame speed due to thermal expansion, which was neglected in the original model. We decouple the model from the full system, determine the necessary corrections for thermal expansion, and then demonstrate that these corrections produce the correct flame speed. The flame-capturing model is an alternative to other popular interface tracking techniques, and might be useful for applications beyond astrophysics.

The Response of Model and Astrophysical Thermonuclear Flames to Curvature and Stretch

Critically understanding the standard candle-like behavior of Type Ia supernovae requires understanding their explosion mechanism. One family of models for Type Ia supernovae begins with a deflagration in a carbon-oxygen white dwarf that greatly accelerates through wrinkling and flame instabilities. While the planar speed and behavior of astrophysically relevant flames is increasingly well understood, more complex behavior, such as the flames response to stretch and curvature, has not been extensively explored in the astrophysical literature; this behavior can greatly enhance or suppress instabilities and local flame-wrinkling, which in turn can increase or decrease the bulk burning rate. In this paper, we explore the effects of curvature on both nuclear flames and simpler model flames to understand the effect of curvature on the flame structure and speed.