26 research outputs found
Eddy diffusivities of inertial particles under gravity
The large-scale/long-time transport of inertial particles of arbitrary mass
density under gravity is investigated by means of a formal multiple-scale
perturbative expansion in the scale-separation parametre between the carrier
flow and the particle concentration field. The resulting large-scale equation
for the particle concentration is determined, and is found to be diffusive with
a positive-definite eddy diffusivity. The calculation of the latter tensor is
reduced to the resolution of an auxiliary differential problem, consisting of a
coupled set of two differential equations in a (6+1)-dimensional coordinate
system (3 space coordinates plus 3 velocity coordinates plus time). Although
expensive, numerical methods can be exploited to obtain the eddy diffusivity,
for any desirable non-perturbative limit (e.g. arbitrary Stokes and Froude
numbers). The aforementioned large-scale equation is then specialized to deal
with two different relevant perturbative limits: i) vanishing of both Stokes
time and sedimenting particle velocity; ii) vanishing Stokes time and finite
sedimenting particle velocity. Both asymptotics lead to a greatly simplified
auxiliary differential problem, now involving only space coordinates and thus
easy to be tackled by standard numerical techniques. Explicit, exact
expressions for the eddy diffusivities have been calculated, for both
asymptotics, for the class of parallel flows, both static and time-dependent.
This allows us to investigate analytically the role of gravity and inertia on
the diffusion process by varying relevant features of the carrier flow, as e.g.
the form of its temporal correlation function. Our results exclude a universal
role played by gravity and inertia on the diffusive behaviour: regimes of both
enhanced and reduced diffusion may exist, depending on the detailed structure
of the carrier flow.Comment: 8 figures (12 plots), submitted to JF
Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
The field theoretic renormalization group and operator product expansion are
applied to the model of a passive scalar quantity advected by a non-Gaussian
velocity field with finite correlation time. The velocity is governed by the
Navier--Stokes equation, subject to an external random stirring force with the
correlation function . It is shown that
the scalar field is intermittent already for small , its structure
functions display anomalous scaling behavior, and the corresponding exponents
can be systematically calculated as series in . The practical
calculation is accomplished to order (two-loop approximation),
including anisotropic sectors. Like for the well-known Kraichnan's rapid-change
model, the anomalous scaling results from the existence in the model of
composite fields (operators) with negative scaling dimensions, identified with
the anomalous exponents. Thus the mechanism of the origin of anomalous scaling
appears similar for the Gaussian model with zero correlation time and
non-Gaussian model with finite correlation time. It should be emphasized that,
in contrast to Gaussian velocity ensembles with finite correlation time, the
model and the perturbation theory discussed here are manifestly Galilean
covariant. The relevance of these results for the real passive advection,
comparison with the Gaussian models and experiments are briefly discussed.Comment: 25 pages, 1 figur
Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations
In melt-blowing very thin liquid fiber jets are spun due to high-velocity air
streams. In literature there is a clear, unsolved discrepancy between the
measured and computed jet attenuation. In this paper we will verify numerically
that the turbulent velocity fluctuations causing a random aerodynamic drag on
the fiber jets -- that has been neglected so far -- are the crucial effect to
close this gap. For this purpose, we model the velocity fluctuations as vector
Gaussian random fields on top of a k-epsilon turbulence description and develop
an efficient sampling procedure. Taking advantage of the special covariance
structure the effort of the sampling is linear in the discretization and makes
the realization possible
Subtle statistical behavior in simple models for random advection-diffusion
Simple models for advection-diffusion with a statistical velocity field are studied here. These models involve advection by a time-independent random shear flow together with a constant mean flow. Several new and surprisingly subtle phenomena are developed here for the statistical behavior in these models. These new phenomena include: 1) mathematical criteria and examples with ill-posed evolution equations for the second order correlations and the mean statistics; 2) explicit sensitive dependence of the large scale, long time renormalization theory on parameters of the problem, such as the mean flow, the infrared cut-off, and the molecular diffusivity, for both the second order correlations and the mean statistics. This surprising sensitive dependence is explained in a self-consistent fashion both through mathematical theory and explicit examples
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Spectral methods for mesoscopic models of pattern formation
In this paper we present spectral algorithms for the solution of mesoscopic equations describing a broad class of pattern formation mechanisms, focusing on a prototypical system of surface processes. These models are in principle stochastic integrodifferential equations and are derived directly from microscopic lattice models, containing detailed information on particle–particle interactions and particle dynamics. The enhanced computational efficiency and accuracy of spectral methods versus finite difference methods are also described
Recommended from our members
Spectral methods for mesoscopic models of pattern formation
In this paper we present spectral algorithms for the solution of mesoscopic equations describing a broad class of pattern formation mechanisms, focusing on a prototypical system of surface processes. These models are in principle stochastic integrodifferential equations and are derived directly from microscopic lattice models, containing detailed information on particle–particle interactions and particle dynamics. The enhanced computational efficiency and accuracy of spectral methods versus finite difference methods are also described