958 research outputs found
Eulerian and modified Lagrangian approaches to multi-dimensional condensation and collection
Turbulence is argued to play a crucial role in cloud droplet growth. The
combined problem of turbulence and cloud droplet growth is numerically
challenging. Here, an Eulerian scheme based on the Smoluchowski equation is
compared with two Lagrangian superparticle (or su- perdroplet) schemes in the
presence of condensation and collection. The growth processes are studied
either separately or in combination using either two-dimensional turbulence, a
steady flow, or just gravitational acceleration without gas flow. Good
agreement between the differ- ent schemes for the time evolution of the size
spectra is observed in the presence of gravity or turbulence. Higher moments of
the size spectra are found to be a useful tool to characterize the growth of
the largest drops through collection. Remarkably, the tails of the size spectra
are reasonably well described by a gamma distribution in cases with gravity or
turbulence. The Lagrangian schemes are generally found to be superior over the
Eulerian one in terms of computational performance. However, it is shown that
the use of interpolation schemes such as the cloud-in-cell algorithm is
detrimental in connection with superparticle or superdroplet approaches.
Furthermore, the use of symmetric over asymmetric collection schemes is shown
to reduce the amount of scatter in the results.Comment: 36 pages, 17 figure
Evolving turbulence and magnetic fields in galaxy clusters
We discuss, using simple analytical models and MHD simulations, the origin
and parameters of turbulence and magnetic fields in galaxy clusters. Three
physically distinct regimes can be identified in the evolution of cluster
turbulence and magnetic fields. Firstly, the fluctuation dynamo will produce
microgauss-strong, random magnetic fields during cluster formation and major
mergers. Turbulent velocity of about 300 km/s can be maintained at scales
100-200 kpc. The magnetic field is intermittent, has a smaller scale of 20-30
kpc and average strength of 2 microgauss. Secondly, when major mergers end,
turbulent speed and magnetic field undergo a power-law decay, decreasing in
strength but increasing in scale by a factor of about two. Thirdly,
smaller-mass subclusters and cluster galaxies produce turbulent wakes, with
turbulent speeds and magnetic field strengths similar to those quoted above.
The velocity scales are about 200 kpc and 10 kpc respectively, and the magnetic
field scale is about 6 times smaller. Although these wakes may fill only a
small fraction of the cluster volume, their area covering factor can be close
to unity. So one can potentially reconcile observations that indicate the
coexistence of turbulence with ordered filamentary gas structures, as in the
Perseus cluster. Random Faraday rotation measure is estimated to be typically
100-200 rad/m^2, in agreement with observations. We predict detectable
synchrotron polarization from cluster radio halos at wavelengths 3-6 cm, if
observed at sufficiently high resolution (abridged).Comment: 20 pages, 9 figures, Replaced to match version accepted by MNRA
Shearing and embedding box simulations of the magnetorotational instability
Two different computational approaches to the magnetorotational instability
(MRI) are pursued: the shearing box approach which is suited for local
simulations and the embedding box approach whereby a Taylor Couette flow is
embedded in a box so that numerical problems with the coordinate singularity
are avoided. New shearing box simulations are presented and differences between
regular and hyperviscosity are discussed. Preliminary simulations of spherical
nonlinear Taylor Couette flow in an embedding box are presented and the effects
of an axial field on the background flow are studied.Comment: to appear in "Hydromagnetic rotating-flow experiments", eds. A.
Bonanno, AI
Effect of turbulence on collisional growth of cloud droplets
We investigate the effect of turbulence on the collisional growth of um-sized
droplets through high- resolution numerical simulations with well resolved
Kolmogorov scales, assuming a collision and coalescence efficiency of unity.
The droplet dynamics and collisions are approximated using a superparticle
approach. In the absence of gravity, we show that the time evolution of the
shape of the droplet-size distribution due to turbulence-induced collisions
depends strongly on the turbulent energy-dissipation rate, but only weakly on
the Reynolds number. This can be explained through the energy dissipation rate
dependence of the mean collision rate described by the Saffman-Turner collision
model. Consistent with the Saffman-Turner collision model and its extensions,
the collision rate increases as the square root of the energy dissipation rate
even when coalescence is invoked. The size distribution exhibits power law
behavior with a slope of -3.7 between a maximum at approximately 10 um up to
about 40 um. When gravity is invoked, turbulence is found to dominate the time
evolution of an initially monodisperse droplet distribution at early times. At
later times, however, gravity takes over and dominates the collisional growth.
We find that the formation of large droplets is very sensitive to the turbulent
energy dissipation rate. This is due to the fact that turbulence enhances the
collisional growth between similar sized droplets at the early stage of
raindrop formation. The mean collision rate grows exponentially, which is
consistent with the theoretical prediction of the continuous collisional growth
even when turbulence-generated collisions are invoked. This consistency only
reflects the mean effect of turbulence on collisional growth
Varying the forcing scale in low Prandtl number dynamos
Small-scale dynamos are expected to operate in all astrophysical fluids that
are turbulent and electrically conducting, for example the interstellar medium,
stellar interiors, and accretion disks, where they may also be affected by or
competing with large-scale dynamos. However, the possibility of small-scale
dynamos being excited at small and intermediate ratios of viscosity to magnetic
diffusivity (the magnetic Prandtl number) has been debated, and the possibility
of them depending on the large-scale forcing wavenumber has been raised. Here
we show, using four values of the forcing wavenumber, that the small-scale
dynamo does not depend on the scale-separation between the size of the
simulation domain and the integral scale of the turbulence, i.e., the forcing
scale. Moreover, the spectral bottleneck in turbulence, which has been implied
as being responsible for raising the excitation conditions of small-scale
dynamos, is found to be invariant under changing the forcing wavenumber.
However, when forcing at the lowest few wavenumbers, the effective forcing
wavenumber that enters in the definition of the magnetic Reynolds number is
found to be about twice the minimum wavenumber of the domain. Our work is
relevant to future studies of small-scale dynamos, of which several
applications are being discussed.Comment: 8 pages, 5 figures, MNRAS, resubmitte
On the Saturation of Astrophysical Dynamos: Numerical Experiments with the No-cosines flow
In the context of astrophysical dynamos we illustrate that the no-cosines
flow, with zero mean helicity, can drive fast dynamo action and study the
dynamo's mode of operation during both the linear and non-linear saturation
regime: It turns out that in addition to a high growth rate in the linear
regime, the dynamo saturates at a level significantly higher than normal
turbulent dynamos, namely at exact equipartition when the magnetic Prandtl
number is on the order of unity. Visualization of the magnetic and velocity
fields at saturation will help us to understand some of the aspects of the
non-linear dynamo problem.Comment: 8 pages, 5 figures, submitted to the proceedings of "Space Climate 1"
to be peer-reviewed to Solar Physic
The onset of a small-scale turbulent dynamo at low magnetic Prandtl numbers
We study numerically the dependence of the critical magnetic Reynolds number
Rmc for the turbulent small-scale dynamo on the hydrodynamic Reynolds number
Re. The turbulence is statistically homogeneous, isotropic, and
mirror--symmetric. We are interested in the regime of low magnetic Prandtl
number Pm=Rm/Re<1, which is relevant for stellar convective zones, protostellar
disks, and laboratory liquid-metal experiments. The two asymptotic
possibilities are Rmc->const as Re->infinity (a small-scale dynamo exists at
low Pm) or Rmc/Re=Pmc->const as Re->infinity (no small-scale dynamo exists at
low Pm). Results obtained in two independent sets of simulations of MHD
turbulence using grid and spectral codes are brought together and found to be
in quantitative agreement. We find that at currently accessible resolutions,
Rmc grows with Re with no sign of approaching a constant limit. We reach the
maximum values of Rmc~500 for Re~3000. By comparing simulations with Laplacian
viscosity, fourth-, sixth-, and eighth-order hyperviscosity and Smagorinsky
large-eddy viscosity, we find that Rmc is not sensitive to the particular form
of the viscous cutoff. This work represents a significant extension of the
studies previously published by Schekochihin et al. 2004, PRL 92, 054502 and
Haugen et al. 2004, PRE, 70, 016308 and the first detailed scan of the
numerically accessible part of the stability curve Rmc(Re).Comment: 4 pages, emulateapj aastex, 2 figures; final version as published in
ApJL (but with colour figures
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