63 research outputs found
Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence
Elastic turbulence is a chaotic regime that emerges in polymer solutions at
low Reynolds numbers. A common way to ensure stability in numerical simulations
of polymer solutions is to add artificially large polymer-stress diffusion. In
order to assess the accuracy of this approach in the elastic-turbulence regime,
we compare numerical simulations of the two-dimensional Oldroyd-B and FENE-P
models sustained by a cellular force with and without artificial diffusion. We
find that artificial diffusion can have a dramatic effect even on the
large-scale properties of the flow and we show some of the spurious phenomena
that may arise when artificial diffusion is used.Comment: 17 page
Deformation of a flexible polymer in a random flow with long correlation time
The effects induced by long temporal correlations of the velocity gradients
on the dynamics of a flexible polymer are investigated by means of theoretical
and numerical analysis of the Hookean and FENE dumbbell models in a random
renewing flow. For Hookean dumbbells, we show that long temporal correlations
strongly suppress the Weissenberg-number dependence of the power-law tail
characterising the probability density function (PDF) of the elongation. For
the FENE model, the PDF becomes bimodal, and the coil-stretch transition occurs
through the simultaneous drop and rise of the two peaks associated with the
coiled and stretched configurations, respectively.Comment: 10 page
Droplets in isotropic turbulence: deformation and breakup statistics
The statistics of the deformation and breakup of neutrally buoyant
sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of
homogeneous isotropic turbulence. The mean lifetime of a drop is also studied
as a function of the initial drop size and the capillary number. A vector model
of drop previously introduced by Olbricht, Rallison and Leal [J. Non-Newtonian
Fluid Mech. , 291 (1982)] is used to predict the behaviour of the
above quantities analytically.Comment: 16 pages, 16 figure
Elastic turbulence in a shell model of polymer solution
We show that, at low inertia and large elasticity, shell models of
viscoelastic fluids develop a chaotic behaviour with properties similar to
those of elastic turbulence. The low dimensionality of shell models allows us
to explore a wide range both in polymer concentration and in Weissenberg
number. Our results demonstrate that the physical mechanisms at the origin of
elastic turbulence do not rely on the boundary conditions or on the geometry of
the mean flow.Comment: 6 pages; 8 figure
Elliptical Tracers in Two-dimensional, Homogeneous, Isotropic Fluid Turbulence: the Statistics of Alignment, Rotation, and Nematic Order
We study the statistical properties of orientation and rotation dynamics of
elliptical tracer particles in two-dimensional, homogeneous and isotropic
turbulence by direct numerical simulations. We consider both the cases in which
the turbulent flow is generated by forcing at large and intermediate length
scales. We show that the two cases are qualitatively different. For large-scale
forcing, the spatial distribution of particle orientations forms large-scale
structures, which are absent for intermediate-scale forcing. The alignment with
the local directions of the flow is much weaker in the latter case than in the
former. For intermediate-scale forcing, the statistics of rotation rates
depends weakly on the Reynolds number and on the aspect ratio of particles. In
contrast with what is observed in three-dimensional turbulence, in two
dimensions the mean-square rotation rate decreases as the aspect ratio
increases.Comment: 5 pages, 6 figure
Bending dynamics of semi-flexible macromolecules in isotropic turbulence
We study the Lagrangian dynamics of semi-flexible macromolecules in laminar
as well as in homogeneous and isotropic turbulent flows by means of
analytically solvable stochastic models and direct numerical simulations. The
statistics of the bending angle is qualitatively different in laminar and
turbulent flows and exhibits a strong dependence on the topology of the
velocity field. In particular, in two-dimensional turbulence, particles are
either found in a fully extended or in a fully folded configuration; in three
dimensions, the predominant configuration is the fully extended one.Comment: 5 pages, 4 figure
Kazantsev dynamo in turbulent compressible flows
We consider the kinematic fluctuation dynamo problem in a flow that is
random, white-in-time, with both solenoidal and potential components. This
model is a generalization of the well-studied Kazantsev model. If both the
solenoidal and potential parts have the same scaling exponent, then, as the
compressibility of the flow increases, the growth rate decreases but remains
positive. If the scaling exponents for the solenoidal and potential parts
differ, in particular if they correspond to typical Kolmogorov and Burgers
values, we again find that an increase in compressibility slows down the growth
rate but does not turn it off. The slow down is, however, weaker and the
critical magnetic Reynolds number is lower than when both the solenoidal and
potential components display the Kolmogorov scaling. Intriguingly, we find that
there exist cases, when the potential part is smoother than the solenoidal
part, for which an increase in compressibility increases the growth rate. We
also find that the critical value of the scaling exponent above which a dynamo
is seen is unity irrespective of the compressibility. Finally, we realize that
the dimension is special, since for all other values of the
critical exponent is higher and depends on the compressibility.Comment: 12 pages, 6 figure
Orientation of non-spherical particles in an axisymmetric random flow
The dynamics of non-spherical rigid particles immersed in an axisymmetric
random flow is studied analytically. The motion of the particles is described
by Jeffery's equation; the random flow is Gaussian and has short correlation
time.The stationary probability density function of orientations is calculated
exactly. Four regimes are identified depending on the statistical anisotropy of
the flow and on the geometrical shape of the particle. If {\lambda} is the axis
of symmetry of the flow, the four regimes are: rotation about {\lambda},
tumbling motion between {\lambda} and -{\lambda}, combination of rotation and
tumbling, and preferential alignment with a direction oblique to {\lambda}.Comment: 18 pages, 8 figure
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