279 research outputs found
Dynamics of fingering convection I: Small-scale fluxes and large-scale instabilities
Double-diffusive instabilities are often invoked to explain enhanced
transport in stably-stratified fluids. The most-studied natural manifestation
of this process, fingering convection, commonly occurs in the ocean's
thermocline and typically increases diapycnal mixing by two orders of magnitude
over molecular diffusion. Fingering convection is also often associated with
structures on much larger scales, such as thermohaline intrusions, gravity
waves and thermohaline staircases. In this paper, we present an exhaustive
study of the phenomenon from small to large scales. We perform the first
three-dimensional simulations of the process at realistic values of the heat
and salt diffusivities and provide accurate estimates of the induced turbulent
transport. Our results are consistent with oceanic field measurements of
diapycnal mixing in fingering regions. We then develop a generalized mean-field
theory to study the stability of fingering systems to large-scale
perturbations, using our calculated turbulent fluxes to parameterize
small-scale transport. The theory recovers the intrusive instability, the
collective instability, and the gamma-instability as limiting cases. We find
that the fastest-growing large-scale mode depends sensitively on the ratio of
the background gradients of temperature and salinity (the density ratio). While
only intrusive modes exist at high density ratios, the collective and
gamma-instabilities dominate the system at the low density ratios where
staircases are typically observed. We conclude by discussing our findings in
the context of staircase formation theory.Comment: 23 pages, 9 figures, submitted to JF
Length scales, collective modes, and type-1.5 regimes in three-band superconductors
The recent discovery of iron pnictide superconductors has resulted in a
rapidly growing interest in multiband models with more than two bands. In this
work we specifically focus on the properties of three-band Ginzburg-Landau
models which do not have direct counterparts in more studied two-band models.
First we derive normal modes and characteristic length scales in the
conventional U(1) three-band Ginzburg-Landau model as well as in its time
reversal symmetry broken counterpart with symmetry. We show
that in the latter case, the normal modes are mixed phase/density collective
excitations. A possibility of the appearance of a massless phase-difference
mode associated with fluctuations of the phase difference is also discussed.
Next we show that gradients of densities and phase differences can be
inextricably intertwined in vortex excitations in three-band models. This can
lead to very long-range attractive intervortex interactions and appearance of
type-1.5 regimes even when the intercomponent Josephson coupling is large. In
some cases it also results in the formation of a domain-like structures in the
form of a ring of suppressed density around a vortex across which one of the
phases shifts by . We also show that field-induced vortices can lead to a
change of broken symmetry from U(1) to in the system. In the
type-1.5 regime, it results in a semi-Meissner state where the system has a
macroscopic phase separation in domains with broken U(1) and
symmetries.Comment: Version 3: Corrected som inconstancies in the parameter set in Fig.2
Also som minor typos corrected. No changes to results or conclusion
Stability Analysis of The Twisted Superconducting Semilocal Strings
We study the stability properties of the twisted vortex solutions in the
semilocal Abelian Higgs model with a global invariance. This
model can be viewed as the Weinberg-Salam theory in the limit where the
non-Abelian gauge field decouples, or as a two component Ginzburg-Landau
theory. The twisted vortices are characterized by a constant global current
, and for they reduce to the semilocal strings, that
is to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model.
Solutions with are more complex and, in particular, they are
{\it less energetic} than the semilocal strings, which makes one hope that they
could have better stability properties. We consider the generic field
fluctuations around the twisted vortex within the linear perturbation theory
and apply the Jacobi criterion to test the existence of the negative modes in
the spectrum of the fluctuation operator. We find that twisted vortices do not
have the homogeneous instability known for the semilocal strings, neither do
they have inhomogeneous instabilities whose wavelength is less than a certain
critical value. This implies that short enough vortex pieces are perturbatively
stable and suggests that small vortex loops could perhaps be stable as well.
For longer wavelength perturbations there is exactly one negative mode in the
spectrum whose growth entails a segmentation of the uniform vortex into a
non-uniform, `sausage like' structure. This instability is qualitatively
similar to the hydrodynamical Plateau-Rayleigh instability of a water jet or to
the Gregory-Laflamme instability of black strings in the theory of gravity in
higher dimensions.Comment: 33 pages, 6 figures. to appear in Nuclear Physics
Dynamics of fingering convection II: The formation of thermohaline staircases
Regions of the ocean's thermocline unstable to salt fingering are often
observed to host thermohaline staircases, stacks of deep well-mixed convective
layers separated by thin stably-stratified interfaces. Decades after their
discovery, however, their origin remains controversial. In this paper we use 3D
direct numerical simulations to shed light on the problem. We study the
evolution of an analogous double-diffusive system, starting from an initial
statistically homogeneous fingering state and find that it spontaneously
transforms into a layered state. By analysing our results in the light of the
mean-field theory developed in Paper I, a clear picture of the sequence of
events resulting in the staircase formation emerges. A collective instability
of homogeneous fingering convection first excites a field of gravity waves,
with a well-defined vertical wavelength. However, the waves saturate early
through regular but localized breaking events, and are not directly responsible
for the formation of the staircase. Meanwhile, slower-growing, horizontally
invariant but vertically quasi-periodic gamma-modes are also excited and grow
according to the gamma-instability mechanism. Our results suggest that the
nonlinear interaction between these various mean-field modes of instability
leads to the selection of one particular gamma-mode as the staircase
progenitor. Upon reaching a critical amplitude, this progenitor overturns into
a fully-formed staircase. We conclude by extending the results of our
simulations to real oceanic parameter values, and find that the progenitor
gamma-mode is expected to grow on a timescale of a few hours, and leads to the
formation of a thermohaline staircase in about one day with an initial spacing
of the order of one to two metres.Comment: 18 pages, 9 figures, associated mpeg file at
http://earth.uni-muenster.de/~stellma/movie_small.mp4, submitted to JF
The Sun's meridional circulation and interior magnetic field
To date, no self-consistent numerical simulation of the solar interior has
succeeded in reproducing the observed thinness of the solar tachocline, and the
persistence of uniform rotation beneath it. Although it is known that the
uniform rotation can be explained by the presence of a global-scale confined
magnetic field, numerical simulations have thus far failed to produce any
solution where such a field remains confined against outward diffusion. We
argue that the problem lies in the choice of parameters for which these
numerical simulations have been performed. We construct a simple analytical
magneto-hydrodynamic model of the solar interior and identify several distinct
parameter regimes. For realistic solar parameter values, our results are in
broad agreement with the tachocline model of Gough & McIntyre. In this regime,
meridional flows driven at the base of the convection zone are of sufficient
amplitude to hold back the interior magnetic field against diffusion. For the
parameter values used in existing numerical simulations, on the other hand, we
find that meridional flows are significantly weaker and, we argue, unable to
confine the interior field. We propose a method for selecting parameter values
in future numerical models.Comment: 49 pages, 11 figures, in press in the Astrophysical Journa
Stable Cosmic Vortons
We present for the first time solutions in the gauged model
of Witten describing vortons -- spinning flux loops stabilized against
contraction by the centrifugal force. Vortons were heuristically described many
years ago, however, the corresponding field theory solutions were not obtained
and so the stability issue remained open. We construct explicitly a family of
stationary vortons characterized by their charge and angular momentum. Most of
them are unstable and break in pieces when perturbed. However, thick vortons
with small radius preserve their form in the 3+1 non-linear dynamical
evolution. This gives the first ever evidence of stable vortons and impacts
several branches of physics where they could potentially exist. These range
from cosmology, since vortons could perhaps contribute to dark matter, to QCD
and condensed matter physics.Comment: 8 pages, 5 figures, improved and extended as compared to the first
version, publishe
On the penetration of meridional circulation below the solar convection zone
Meridional flows with velocities of a few meters per second are observed in
the uppermost regions of the solar convection zone. The amplitude and pattern
of the flows deeper in the solar interior, in particular near the top of the
radiative region, are of crucial importance to a wide range of solar
magnetohydrodynamical processes. In this paper, we provide a systematic study
of the penetration of large-scale meridional flows from the convection zone
into the radiative zone. In particular, we study the effects of the assumed
boundary conditions applied at the convective-radiative interface on the deeper
flows. Using simplified analytical models in conjunction with more complete
numerical methods, we show that penetration of the convectively-driven
meridional flows into the deeper interior is not necessarily limited to a
shallow Ekman depth but can penetrate much deeper, depending on how the
convective-radiative interface flows are modeled.Comment: 13 pages, 5 figures. Subitted to Ap
Stability Analysis of Superconducting Electroweak Vortices
We carry out a detailed stability analysis of the superconducting vortex
solutions in the Weinberg-Salam theory described in Nucl.Phys. B826 (2010) 174.
These vortices are characterized by constant electric current and electric
charge density , for they reduce to Z strings. We consider the
generic field fluctuations around the vortex and apply the functional Jacobi
criterion to detect the negative modes in the fluctuation operator spectrum. We
find such modes and determine their dispersion relation, they turn out to be of
two different types, according to their spatial behavior. There are
non-periodic in space negative modes, which can contribute to the instability
of infinitely long vortices, but they can be eliminated by imposing the
periodic boundary conditions along the vortex. There are also periodic negative
modes, but their wavelength is always larger than a certain minimal value, so
that they cannot be accommodated by the short vortex segments. However, even
for the latter there remains one negative mode responsible for the homogeneous
expansion instability. This mode may probably be eliminated when the vortex
segment is bent into a loop. This suggests that small vortex loops balanced
against contraction by the centrifugal force could perhaps be stable.Comment: 42 pages, 11 figure
Individual and collective behavior of dust particles in a protoplanetary nebula
We study the interaction between gas and dust particles in a protoplanetary
disk, comparing analytical and numerical results. We first calculate
analytically the trajectories of individual particles undergoing gas drag in
the disk, in the asymptotic cases of very small particles (Epstein regime) and
very large particles (Stokes regime). Using a Boltzmann averaging method, we
then infer their collective behavior. We compare the results of this analytical
formulation against numerical computations of a large number of particles.
Using successive moments of the Boltzmann equation, we derive the equivalent
fluid equations for the average motion of the particles; these are
intrinsically different in the Epstein and Stokes regimes. We are also able to
study analytically the temporal evolution of a collection of particles with a
given initial size-distribution provided collisions are ignored.Comment: 15 pages, 9 figures, submitted to Ap
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