347 research outputs found
On how a joint interaction of two innocent partners (smooth advection & linear damping) produces a strong intermittency
Forced advection of passive scalar by a smooth -dimensional incompressible
velocity in the presence of a linear damping is studied. Acting separately
advection and dumping do not lead to an essential intermittency of the steady
scalar statistics, while being mixed together produce a very strong
non-Gaussianity in the convective range: -th (positive) moment of the
absolute value of scalar difference,
is proportional to , , where measures the rate of the damping in the units
of the stretching rate. Probability density function (PDF) of the scalar
difference is also found.Comment: 4 pages, RevTex, Submitted to Phys. Fluid
Dynamics of Fluctuation Dominated Phase Ordering: Hard-core Passive Sliders on a Fluctuating Surface
We study the dynamics of a system of hard-core particles sliding downwards on
a one dimensional fluctuating interface, which in a special case can be mapped
to the problem of a passive scalar advected by a Burgers fluid. Driven by the
surface fluctuations, the particles show a tendency to cluster, but the
hard-core interaction prevents collapse. We use numerical simulations to
measure the auto-correlation function in steady state and in the aging regime,
and space-time correlation functions in steady state. We have also calculated
these quantities analytically in a related surface model. The steady state
auto-correlation is a scaling function of t/L^z, where L is the system size and
z the dynamic exponent. Starting from a finite intercept, the scaling function
decays with a cusp, in the small argument limit. The finite value of the
intercept indicates the existence of long range order in the system. The
space-time correlation, which is a function of r/L and t/L^z, is non-monotonic
in t for fixed r. The aging auto-correlation is a scaling function of t_1 and
t_2 where t_1 is the waiting time and t_2 the time difference. This scaling
function decays as a power law for t_2 \gg t_1; for t_1 \gg t_2, it decays with
a cusp as in steady state. To reconcile the occurrence of strong fluctuations
in the steady state with the fact of an ordered state, we measured the
distribution function of the length of the largest cluster. This shows that
fluctuations never destroy ordering, but rather the system meanders from one
ordered configuration to another on a relatively rapid time scale
Statistical geometry in scalar turbulence
A general link between geometry and intermittency in passive scalar
turbulence is established. Intermittency is qualitatively traced back to events
where tracer particles stay for anomalousy long times in degenerate geometries
characterized by strong clustering. The quantitative counterpart is the
existence of special functions of particle configurations which are
statistically invariant under the flow. These are the statistical integrals of
motion controlling the scalar statistics at small scales and responsible for
the breaking of scale invariance associated to intermittency.Comment: 4 pages, 5 figure
Non-universality of the scaling exponents of a passive scalar convected by a random flow
We consider passive scalar convected by multi-scale random velocity field
with short yet finite temporal correlations. Taking Kraichnan's limit of a
white Gaussian velocity as a zero approximation we develop perturbation theory
with respect to a small correlation time and small non-Gaussianity of the
velocity. We derive the renormalization (due to temporal correlations and
non-Gaussianity) of the operator of turbulent diffusion. That allows us to
calculate the respective corrections to the anomalous scaling exponents of the
scalar field and show that they continuously depend on velocity correlation
time and the degree of non-Gaussianity. The scalar exponents are thus non
universal as was predicted by Shraiman and Siggia on a phenomenological ground
(CRAS {\bf 321}, 279, 1995).Comment: 4 pages, RevTex 3.0, Submitted to Phys.Rev.Let
Statistical conservation laws in turbulent transport
We address the statistical theory of fields that are transported by a
turbulent velocity field, both in forced and in unforced (decaying)
experiments. We propose that with very few provisos on the transporting
velocity field, correlation functions of the transported field in the forced
case are dominated by statistically preserved structures. In decaying
experiments (without forcing the transported fields) we identify infinitely
many statistical constants of the motion, which are obtained by projecting the
decaying correlation functions on the statistically preserved functions. We
exemplify these ideas and provide numerical evidence using a simple model of
turbulent transport. This example is chosen for its lack of Lagrangian
structure, to stress the generality of the ideas
The intermittent behavior and hierarchical clustering of the cosmic mass field
The hierarchical clustering model of the cosmic mass field is examined in the
context of intermittency. We show that the mass field satisfying the
correlation hierarchy is intermittent if , where is the dimension of the field, and is the power-law
index of the non-linear power spectrum in the discrete wavelet transform (DWT)
representation. We also find that a field with singular clustering can be
described by hierarchical clustering models with scale-dependent coefficients
and that this scale-dependence is completely determined by the
intermittent exponent and . Moreover, the singular exponents of a field
can be calculated by the asymptotic behavior of when is large.
Applying this result to the transmitted flux of HS1700 Ly forests, we
find that the underlying mass field of the Ly forests is significantly
intermittent. On physical scales less than about 2.0 h Mpc, the observed
intermittent behavior is qualitatively different from the prediction of the
hierarchical clustering with constant . The observations, however, do show
the existence of an asymptotic value for the singular exponents. Therefore, the
mass field can be described by the hierarchical clustering model with
scale-dependent . The singular exponent indicates that the cosmic mass
field at redshift is weakly singular at least on physical scales as
small as 10 h kpc.Comment: AAS Latex file, 33 pages,5 figures included, accepted for publication
in Ap
Dynamics of a passive sliding particle on a randomly fluctuating surface
We study the motion of a particle sliding under the action of an external
field on a stochastically fluctuating one-dimensional Edwards-Wilkinson
surface. Numerical simulations using the single-step model shows that the
mean-square displacement of the sliding particle shows distinct dynamic scaling
behavior, depending on whether the surface fluctuates faster or slower than the
motion of the particle. When the surface fluctuations occur on a time scale
much smaller than the particle motion, we find that the characteristic length
scale shows anomalous diffusion with , where from numerical data. On the other hand, when the particle moves faster
than the surface, its dynamics is controlled by the surface fluctuations and
. A self-consistent approximation predicts that the
anomalous diffusion exponent is , in good agreement with simulation
results. We also discuss the possibility of a slow cross-over towards
asymptotic diffusive behavior. The probability distribution of the displacement
has a Gaussian form in both the cases.Comment: 6 pages, 4 figures, error in reference corrected and new reference
added, submitted to Phys. Rev.
Passive Sliders on Growing Surfaces and (anti-)Advection in Burger's Flows
We study the fluctuations of particles sliding on a stochastically growing
surface. This problem can be mapped to motion of passive scalars in a randomly
stirred Burger's flow. Renormalization group studies, simulations, and scaling
arguments in one dimension, suggest a rich set of phenomena: If particles slide
with the avalanche of growth sites (advection with the fluid), they tend to
cluster and follow the surface dynamics. However, for particles sliding against
the avalanche (anti-advection), we find slower diffusion dynamics, and density
fluctuations with no simple relation to the underlying fluid, possibly with
continuously varying exponents.Comment: 4 pages revtex
Fronts in passive scalar turbulence
The evolution of scalar fields transported by turbulent flow is characterized
by the presence of fronts, which rule the small-scale statistics of scalar
fluctuations. With the aid of numerical simulations, it is shown that: isotropy
is not recovered, in the classical sense, at small scales; scaling exponents
are universal with respect to the scalar injection mechanisms; high-order
exponents saturate to a constant value; non-mature fronts dominate the
statistics of intense fluctuations. Results on the statistics inside the
plateaux, where fluctuations are weak, are also presented. Finally, we analyze
the statistics of scalar dissipation and scalar fluxes.Comment: 18 pages, 27 figure
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