13,551 research outputs found
3D simulations of Rayleigh-Taylor mixing in core-collapse SNe with CASTRO
We present multidimensional simulations of the post-explosion hydrodynamics
in three different 15 solar mass supernova models with zero, 10^{-4} solar
metallicity, and solar metallicities. We follow the growth of the
Rayleigh-Taylor instability that mixes together the stellar layers in the wake
of the explosion. Models are initialized with spherically symmetric explosions
and perturbations are seeded by the grid. Calculations are performed in
two-dimensional axisymmetric and three-dimensional Cartesian coordinates using
the new Eulerian hydrodynamics code, CASTRO. We find as in previous work, that
Rayleigh-Taylor perturbations initially grow faster in 3D than in 2D. As the
Rayleigh-Taylor fingers interact with one another, mixing proceeds to a greater
degree in 3D than in 2D, reducing the local Atwood number and slowing the
growth rate of the instability in 3D relative to 2D. By the time mixing has
stopped, the width of the mixed region is similar in 2D and 3D simulations
provided the Rayleigh-Taylor fingers show significant interaction. Our results
imply that 2D simulations of light curves and nucleosynthesis in supernovae
(SNe) that die as red giants may capture the features of an initially
spherically symmetric explosion in far less computational time than required by
a full 3D simulation. However, capturing large departures from spherical
symmetry requires a significantly perturbed explosion. Large scale asymmetries
cannot develop through an inverse cascade of merging Rayleigh-Taylor
structures; they must arise from asymmetries in the initial explosion.Comment: 12 pages, 5 figures, ApJ accepte
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Rayleigh-Taylor mixing: confinement by stratification and geometry
Rayleigh-Taylor instability has been an area of active research in fluid dynamics for
the last twenty years, but relatively little attention has been paid to the dynamics
of problems where Rayleigh-Taylor instability plays a role, but is only one component of a more complex system. Here, Rayleigh-Taylor instability between miscible fluids is examined in situations where it is confined by various means: by geometric
restriction, by penetration into a stable linear stratification, and by impingement
on a stable density interface. Water-based experiments are modelled using a variety
of techniques, ranging from simple hand calculation of energy exchange to full
three-dimensional numerical simulation. Since there are well known difficulties in
modelling unconfined Rayleigh-Taylor instability, the confined test cases have been sequenced to begin with dynamically simple benchmark systems on which existing
modelling approaches perform well, then they progress to more complex systems and
explore the limitations of the various models. Some work on the phenomenology of
turbulent mixing is also presented, including a new experimental technique that allows mixed fluid to be visualised directly, and an analysis of energy transport and mixing efficiency in variable density flows dominated by mixing
Scale invariant bounds for mixing in the Rayleigh-Taylor instability
We study the Rayleigh-Taylor instability for two miscible, incompressible,
inviscid fluids. Scale-invariant estimates for the size of the mixing zone and
coarsening of internal structures in the fully nonlinear regime are established
following techniques introduced for the Saffman-Taylor instability in [10].
These bounds provide optimal scaling laws and reveal the strong role of
dissipation in slowing down mixing
Mixing across fluid interfaces compressed by convective flow in porous media
We study the mixing in the presence of convective flow in a porous medium.
Convection is characterized by the formation of vortices and stagnation points,
where the fluid interface is stretched and compressed enhancing mixing. We
analyze the behavior of the mixing dynamics in different scenarios using an
interface deformation model. We show that the scalar dissipation rate, which is
related to the dissolution fluxes, is controlled by interfacial processes,
specifically the equilibrium between interface compression and diffusion, which
depends on the flow field configuration. We consider different scenarios of
increasing complexity. First, we analyze a double-gyre synthetic velocity
field. Second, a Rayleigh-B\'enard instability (the Horton-Rogers-Lapwood
problem), in which stagnation points are located at a fixed interface. This
system experiences a transition from a diffusion controlled mixing to a chaotic
convection as the Rayleigh number increases. Finally, a Rayleigh-Taylor
instability with a moving interface, in which mixing undergoes three different
regimes: diffusive, convection dominated, and convection shutdown. The
interface compression model correctly predicts the behavior of the systems. It
shows how the dependency of the compression rate on diffusion explains the
change in the scaling behavior of the scalar dissipation rate. The model
indicates that the interaction between stagnation points and the correlation
structure of the velocity field is also responsible for the transition between
regimes. We also show the difference in behavior between the dissolution fluxes
and the mixing state of the systems. We observe that while the dissolution flux
decreases with the Rayleigh number, the system becomes more homogeneous. That
is, mixing is enhanced by reducing diffusion. This observation is explained by
the effect of the instability patterns
Lattice Boltzmann Methods for thermal flows: continuum limit and applications to compressible Rayleigh-Taylor systems
We compute the continuum thermo-hydrodynamical limit of a new formulation of
lattice kinetic equations for thermal compressible flows, recently proposed in
[Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the
hydrodynamical manifold is given by the correct compressible Fourier-
Navier-Stokes equations for a perfect fluid. We validate the numerical
algorithm by means of exact results for transition to convection in
Rayleigh-B\'enard compressible systems and against direct comparison with
finite-difference schemes. The method is stable and reliable up to temperature
jumps between top and bottom walls of the order of 50% the averaged bulk
temperature. We use this method to study Rayleigh-Taylor instability for
compressible stratified flows and we determine the growth of the mixing layer
at changing Atwood numbers up to At ~ 0.4. We highlight the role played by the
adiabatic gradient in stopping the mixing layer growth in presence of high
stratification and we quantify the asymmetric growth rate for spikes and
bubbles for two dimensional Rayleigh- Taylor systems with resolution up to Lx
\times Lz = 1664 \times 4400 and with Rayleigh numbers up to Ra ~ 2 \times
10^10.Comment: 26 pages, 13 figure
Rayleigh-Taylor mixing : Direct numerical simulation and implicit large eddy simulation
Previous research into three-dimensional numerical simulation of self-similar mixing due to Rayleigh-Taylor instability is summarized. A range of numerical approaches has been used: direct numerical simulation, implicit large eddy simulation and large eddy simulation with an explicit model for sub-grid-scale dissipation. However, few papers have made direct comparisons between the various approaches. The main purpose of the current paper is to give comparisons of direct numerical simulations and implicit large eddy simulations using the same computational framework. Results are shown for four test cases: (i) single-mode Rayleigh-Taylor instability, (ii) self-similar Rayleigh-Taylor mixing, (iii) three-layer mixing and (iv) a tilted-rig Rayleigh-Taylor experiment. It is found that both approaches give similar results for the high-Reynolds number behavior. Direct numerical simulation is needed to assess the influence of finite Reynolds number
Scrambled and Unscrambled Turbulence
The linked fluid dynamics videos depict Rayleigh-Taylor turbulence when
driven by a complex acceleration profile involving two stages of acceleration
interspersed with a stage of stabilizing deceleration. Rayleigh-Taylor (RT)
instability occurs at the interface separating two fluids of different
densities, when the lighter fluid is accelerated in to the heavier fluid. The
turbulent mixing arising from the development of the miscible RT instability is
of key importance in the design of Inertial Confinement Fusion capsules, and to
the understanding of astrophysical events, such as Type Ia supernovae. By
driving this flow with an accel-decel-accel profile, we have investigated how
structures in RT turbulence are affected by a sudden change in the direction of
the acceleration first from destabilizing acceleration to deceleration, and
followed by a restoration of the unstable acceleration. By studying turbulence
under such highly non-equilibrium conditions, we hope to develop an
understanding of the response and recovery of self-similar turbulence to sudden
changes in the driving acceleration.Comment: 3 pages article, Two videos are include
Scaling of Rayleigh-Taylor mixing in porous media
Pushing two fluids with different density one against the other causes the
development of the Rayleigh-Taylor instability at their interface, which
further evolves in a complex mixing layer. In porous media, this process is
influenced by the viscous resistance experienced while flowing through the
pores, which is described by the Darcy's law. Here, we investigate the mixing
properties of the Darcy-Rayleigh-Taylor system in the limit of large P\'eclet
number by means of direct numerical simulations in three and two dimensions. In
the mixing zone, the balance between gravity and viscous forces results in a
non-self-similar growth of elongated plumes, whose length increases linearly in
time while their width follows a diffusive growth. The mass-transfer Nusselt
number is found to increase linearly with the Darcy-Rayleigh number supporting
a universal scaling in porous convection at high Ra numbers. Finally, we find
that the mixing process displays important quantitative differences between two
and three dimensions.Comment: 7 pages, 3 figure
Simulations of Astrophysical Fluid Instabilities
We present direct numerical simulations of mixing at Rayleigh-Taylor unstable
interfaces performed with the FLASH code, developed at the ASCI/Alliances
Center for Astrophysical Thermonuclear Flashes at the University of Chicago. We
present initial results of single-mode studies in two and three dimensions. Our
results indicate that three-dimensional instabilities grow significantly faster
than two-dimensional instabilities and that grid resolution can have a
significant effect on instability growth rates. We also find that unphysical
diffusive mixing occurs at the fluid interface, particularly in poorly resolved
simulations.Comment: 3 pages, 1 figure. To appear in the proceedings of the 20th Texas
Symposium on Relativistic Astrophysic
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