231 research outputs found
Structures and intermittency in a passive scalar model
A one-dimensional white-in-time passive scalar model is introduced. Strong
and persistent structures are shown to be present. A perturbative expansion for
the scaling exponents is performed around a Gaussian limit of the model. The
resulting predictions are compared with numerical simulations.Comment: 8 pages, 4 figure
Intermittency in passive scalar advection
A Lagrangian method for the numerical simulation of the Kraichnan passive
scalar model is introduced. The method is based on Monte--Carlo simulations of
tracer trajectories, supplemented by a point-splitting procedure for coinciding
points. Clean scaling behavior for scalar structure functions is observed. The
scheme is exploited to investigate the dependence of scalar anomalies on the
scaling exponent of the advecting velocity field. The three-dimensional
fourth-order structure function is specifically considered.Comment: 4 pages, 5 figure
Active vs passive scalar turbulence
Active and passive scalars transported by an incompressible two-dimensional
conductive fluid are investigated. It is shown that a passive scalar displays a
direct cascade towards the small scales while the active magnetic potential
builds up large-scale structures in an inverse cascade process. Correlations
between scalar input and particle trajectories are found to be responsible for
those dramatic differences as well as for the behavior of dissipative
anomalies.Comment: Revised version, Phys. Rev. Lett., in pres
Inference in particle tracking experiments by passing messages between images
Methods to extract information from the tracking of mobile objects/particles
have broad interest in biological and physical sciences. Techniques based on
simple criteria of proximity in time-consecutive snapshots are useful to
identify the trajectories of the particles. However, they become problematic as
the motility and/or the density of the particles increases due to uncertainties
on the trajectories that particles followed during the images' acquisition
time. Here, we report an efficient method for learning parameters of the
dynamics of the particles from their positions in time-consecutive images. Our
algorithm belongs to the class of message-passing algorithms, known in computer
science, information theory and statistical physics as Belief Propagation (BP).
The algorithm is distributed, thus allowing parallel implementation suitable
for computations on multiple machines without significant inter-machine
overhead. We test our method on the model example of particle tracking in
turbulent flows, which is particularly challenging due to the strong transport
that those flows produce. Our numerical experiments show that the BP algorithm
compares in quality with exact Markov Chain Monte-Carlo algorithms, yet BP is
far superior in speed. We also suggest and analyze a random-distance model that
provides theoretical justification for BP accuracy. Methods developed here
systematically formulate the problem of particle tracking and provide fast and
reliable tools for its extensive range of applications.Comment: 18 pages, 9 figure
Shear effects on passive scalar spectra
The effects of a large-scale shear on the energy spectrum of a passively
advected scalar field are investigated. The shear is superimposed on a
turbulent isotropic flow, yielding an Obukhov-Corrsin scalar
spectrum at small scales. Shear effects appear at large scales, where a
different, anisotropic behavior is observed. The scalar spectrum is shown to
behave as for a shear fixed in intensity and direction. For other
types of shear characteristics, the slope is generally intermediate between the
-5/3 Obukhov-Corrsin's and the -1 Batchelor's values. The physical mechanisms
at the origin of this behaviour are illustrated in terms of the motion of
Lagrangian particles. They provide an explanation to the scalar spectra shallow
and dependent on the experimental conditions observed in shear flows at
moderate Reynolds numbers.Comment: 10 LaTeX pages,3 eps Figure
Bifractality of the Devil's staircase appearing in the Burgers equation with Brownian initial velocity
It is shown that the inverse Lagrangian map for the solution of the Burgers
equation (in the inviscid limit) with Brownian initial velocity presents a
bifractality (phase transition) similar to that of the Devil's staircase for
the standard triadic Cantor set. Both heuristic and rigorous derivations are
given. It is explained why artifacts can easily mask this phenomenon in
numerical simulations.Comment: 12 pages, LaTe
Scalar transport in compressible flow
Transport of scalar fields in compressible flow is investigated. The
effective equations governing the transport at scales large compared to those
of the advecting flow are derived by using multi-scale techniques. Ballistic
transport generally takes place when both the solenoidal and the potential
components of the velocity do not vanish, despite of the fact that it has zero
average value. The calculation of the effective ballistic velocity is
reduced to the solution of one auxiliary equation. An analytic expression for
is derived in some special instances, i.e. flows depending on a single
coordinate, random with short correlation times and slightly compressible
cellular flow. The effective mean velocity vanishes for velocity fields
which are either incompressible or potential and time-independent. For generic
compressible flow, the most general conditions ensuring the absence of
ballistic transport are isotropy and/or parity invariance. When vanishes
(or in the frame of reference moving with velocity ), standard diffusive
transport takes place. It is known that diffusion is always enhanced by
incompressible flow. On the contrary, we show that diffusion is depleted in the
presence of time-independent potential flow. Trapping effects due to potential
wells are responsible for this depletion. For time-dependent potential flow or
generic compressible flow, transport rates are enhanced or depleted depending
on the detailed structure of the velocity field.Comment: 27 pages, submitted to Physica
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