228 research outputs found
Diffusion of a passive scalar by convective flows under parametric disorder
We study transport of a weakly diffusive pollutant (a passive scalar) by
thermoconvective flow in a fluid-saturated horizontal porous layer heated from
below under frozen parametric disorder. In the presence of disorder (random
frozen inhomogeneities of the heating or of macroscopic properties of the
porous matrix), spatially localized flow patterns appear below the convective
instability threshold of the system without disorder. Thermoconvective flows
crucially effect the transport of a pollutant along the layer, especially when
its molecular diffusion is weak. The effective (or eddy) diffusivity also
allows to observe the transition from a set of localized currents to an almost
everywhere intense "global" flow. We present results of numerical calculation
of the effective diffusivity and discuss them in the context of localization of
fluid currents and the transition to a "global" flow. Our numerical findings
are in a good agreement with the analytical theory we develop for the limit of
a small molecular diffusivity and sparse domains of localized currents. Though
the results are obtained for a specific physical system, they are relevant for
a broad variety of fluid dynamical systems.Comment: 12 pages, 4 figures, the revised version of the paper for J. Stat.
Mech. (Special issue for proceedings of 5th Intl. Conf. on Unsolved Problems
on Noise and Fluctuations in Physics, Biology & High Technology, Lyon
(France), June 2-6, 2008
Advectional enhancement of eddy diffusivity under parametric disorder
Frozen parametric disorder can lead to appearance of sets of localized
convective currents in an otherwise stable (quiescent) fluid layer heated from
below. These currents significantly influence the transport of an admixture (or
any other passive scalar) along the layer. When the molecular diffusivity of
the admixture is small in comparison to the thermal one, which is quite typical
in nature, disorder can enhance the effective (eddy) diffusivity by several
orders of magnitude in comparison to the molecular diffusivity. In this paper
we study the effect of an imposed longitudinal advection on delocalization of
convective currents, both numerically and analytically; and report subsequent
drastic boost of the effective diffusivity for weak advection.Comment: 14 pages, 6 figures, for Topical Issue of Physica Scripta "2nd Intl.
Conf. on Turbulent Mixing and Beyond
Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability
The influence of small additive noise on structure formation near a forwards
and near an inverted bifurcation as described by a cubic and quintic Ginzburg
Landau amplitude equation, respectively, is studied numerically for group
velocities in the vicinity of the convective-absolute instability where the
deterministic front dynamics would empty the system.Comment: 16 pages, 7 Postscript figure
Attractive Interaction Between Pulses in a Model for Binary-Mixture Convection
Recent experiments on convection in binary mixtures have shown that the
interaction between localized waves (pulses) can be repulsive as well as {\it
attractive} and depends strongly on the relative {\it orientation} of the
pulses. It is demonstrated that the concentration mode, which is characteristic
of the extended Ginzburg-Landau equations introduced recently, allows a natural
understanding of that result. Within the standard complex Ginzburg-Landau
equation this would not be possible.Comment: 7 pages revtex with 3 postscript figures (uuencoded
Sources and sinks separating domains of left- and right-traveling waves: Experiment versus amplitude equations
In many pattern forming systems that exhibit traveling waves, sources and
sinks occur which separate patches of oppositely traveling waves. We show that
simple qualitative features of their dynamics can be compared to predictions
from coupled amplitude equations. In heated wire convection experiments, we
find a discrepancy between the observed multiplicity of sources and theoretical
predictions. The expression for the observed motion of sinks is incompatible
with any amplitude equation description.Comment: 4 pages, RevTeX, 3 figur
Influence of the Soret effect on convection of binary fluids
Convection in horizontal layers of binary fluids heated from below and in
particular the influence of the Soret effect on the bifurcation properties of
extended stationary and traveling patterns that occur for negative Soret
coupling is investigated theoretically. The fixed points corresponding to these
two convection structures are determined for realistic boundary conditions with
a many mode Galerkin scheme for temperature and concentration and an accurate
one mode truncation of the velocity field. This solution procedure yields the
stable and unstable solutions for all stationary and traveling patterns so that
complete phase diagrams for the different convection types in typical binary
liquid mixtures can easily be computed. Also the transition from weakly to
strongly nonlinear states can be analyzed in detail. An investigation of the
concentration current and of the relevance of its constituents shows the way
for a simplification of the mode representation of temperature and
concentration field as well as for an analytically manageable few mode
description.Comment: 30 pages, 12 figure
Thermally Induced Fluctuations Below the Onset of Rayleigh-B\'enard Convection
We report quantitative experimental results for the intensity of
noise-induced fluctuations below the critical temperature difference for Rayleigh-B\'enard convection. The structure factor of the fluctuating
convection rolls is consistent with the expected rotational invariance of the
system. In agreement with predictions based on stochastic hydrodynamic
equations, the fluctuation intensity is found to be proportional to
where . The
noise power necessary to explain the measurements agrees with the prediction
for thermal noise. (WAC95-1)Comment: 13 pages of text and 4 Figures in a tar-compressed and uuencoded file
(using uufiles package). Detailed instructions of unpacking are include
Influence of through-flow on linear pattern formation properties in binary mixture convection
We investigate how a horizontal plane Poiseuille shear flow changes linear
convection properties in binary fluid layers heated from below. The full linear
field equations are solved with a shooting method for realistic top and bottom
boundary conditions. Through-flow induced changes of the bifurcation thresholds
(stability boundaries) for different types of convective solutions are deter-
mined in the control parameter space spanned by Rayleigh number, Soret coupling
(positive as well as negative), and through-flow Reynolds number. We elucidate
the through-flow induced lifting of the Hopf symmetry degeneracy of left and
right traveling waves in mixtures with negative Soret coupling. Finally we
determine with a saddle point analysis of the complex dispersion relation of
the field equations over the complex wave number plane the borders between
absolute and convective instabilities for different types of perturbations in
comparison with the appropriate Ginzburg-Landau amplitude equation
approximation. PACS:47.20.-k,47.20.Bp, 47.15.-x,47.54.+rComment: 19 pages, 15 Postscript figure
Phase chaos in the anisotropic complex Ginzburg-Landau Equation
Of the various interesting solutions found in the two-dimensional complex
Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show
particularly novel features. They exist in a broader parameter range than in
the isotropic case, and often even broader than in one dimension. They
typically represent the global attractor of the system. There exist two
variants of phase chaos: a quasi-one dimensional and a two-dimensional
solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references,
typos removed, accepted as Rapid Commun. in Phys. Rev.
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