230 research outputs found
A quasi-elastic regime for vibrated granular gases
Using simple scaling arguments and two-dimensional numerical simulations of a
granular gas excited by vibrating one of the container boundaries, we study a
double limit of small and large , where is the restitution
coefficient and the size of the container. We show that if the particle
density and where is the particle diameter, are
kept constant and small enough, the granular temperature, i.e. the mean value
of the kinetic energy per particle, , tends to a constant whereas the
mean dissipated power per particle, , decreases like when
increases, provided that . The relative fluctuations
of , and the power injected by the moving boundary, , have simple
properties in that regime. In addition, the granular temperature can be
determined from the fluctuations of the power injected by the moving
boundary.
Clustering of floaters on the free surface of a turbulent flow: an experimental study
We present an experimental study of the statistical properties of
millimeter-size spheres floating on the surface of a turbulent flow. The flow
is generated in a layer of liquid metal by an electromagnetic forcing. By using
two magnet arrays, we are able to create one highly fluctuating flow and
another, more stationary flow. In both cases, we follow the motion of hundreds
of particles floating at the deformed interface of the liquid metal. We
evidence the clustering of floaters by a statistical study of the local
concentration of particles. Some dynamical properties of clusters are exposed.
We perform spatial correlations between particle concentration and
hydrodynamical quantities linked with inertial effects; with vortical motion,
and with horizontal divergence (corresponding to compressibility in the
surface). From comparing these correlations, we propose the so-called surface
compressibility as the main clustering mechanism in our system. Hence, although
floaters are not passive scalar and move on a deformed surface, the scenario is
similar to the one reported for passive scalar on an almost flat free surface
of a turbulent flow.Comment: 11 pages, 7 figures. Accepted to publication in European Journal of
Mechanics B/Fluid
Injected Power Fluctuations in 1D Dissipative Systems
Using fermionic techniques, we compute exactly the large deviation function
(ldf) of the time-integrated injected power in several one-dimensional
dissipative systems of classical spins. The dynamics are T=0 Glauber dynamics
supplemented by an injection mechanism, which is taken as a Poissonian flipping
of one particular spin. We discuss the physical content of the results,
specifically the influence of the rate of the Poisson process on the properties
of the ldf.Comment: 18 pages, 8 figure
Intermittency as a consequence of a stationarity constraint on the energy flux
In his seminal work on turbulence, Kolmogorov made use of the stationary
hypothesis to determine the Power Density Spectrum of the velocity field in
turbulent flows. However to our knowledge, the constraints that stationary
processes impose on the fluctuations of the energy flux have never been used in
the context of turbulence. Here we recall that the Power Density Spectra of the
fluctuations of the injected power, the dissipated power and the energy flux
have to converge to a common value at vanishing frequency. Hence, we show that
the intermittent GOY--shell model fulfills these constraints. We argue that
they can be related to intermittency. Indeed, we find that the constraint on
the fluctuations of the energy flux implies a relation between the scaling
exponents that characterize intermittency, which is verified by the GOY--shell
model and in agreement with the She-Leveque formula. It also fixes the
intermittency parameter of the log-normal model at a realistic value. The
relevance of these results for real turbulence is drawn in the concluding
remarks.Comment: 5 pages, 4 figures, 23 reference
Energy fluctuations in vibrated and driven granular gases
We investigate the behavior of energy fluctuations in several models of
granular gases maintained in a non-equilibrium steady state. In the case of a
gas heated from a boundary, the inhomogeneities of the system play a
predominant role. Interpreting the total kinetic energy as a sum of independent
but not identically distributed random variables, it is possible to compute the
probability density function (pdf) of the total energy. Neglecting correlations
and using the analytical expression for the inhomogeneous temperature profile
obtained from the granular hydrodynamic equations, we recover results which
have been previously observed numerically and which had been attributed to the
presence of correlations. In order to separate the effects of spatial
inhomogeneities from those ascribable to velocity correlations, we have also
considered two models of homogeneously thermostated gases: in this framework it
is possible to reveal the presence of non-trivial effects due to velocity
correlations between particles. Such correlations stem from the inelasticity of
collisions. Moreover, the observation that the pdf of the total energy tends to
a Gaussian in the large system limit, suggests that they are also due to the
finite size of the system.Comment: 13 pages, 10 figure
Low frequency spectra of bending wave turbulence
We study experimentally the dynamics of long waves among turbulent bending
waves in a thin elastic plate set into vibration by a monochromatic forcing at
a frequency . This frequency is chosen large compared with the
characteristic frequencies of bending waves. As a consequence, a range of
conservative scales, without energy flux in average, exists for frequencies
. Within this range, we report a flat power density spectrum for the
orthogonal velocity, corresponding to energy equipartition between modes. Thus,
the average energy per mode -- analogous to a temperature -- fully
characterizes the large-scale turbulent wave field. We present an expression
for as a function of the forcing frequency and amplitude, and of the
plate characteristics
Effects of the low frequencies of noise on On-Off intermittency
A bifurcating system subject to multiplicative noise can exhibit on-off
intermittency close to the instability threshold. For a canonical system, we
discuss the dependence of this intermittency on the Power Spectrum Density
(PSD) of the noise. Our study is based on the calculation of the Probability
Density Function (PDF) of the unstable variable. We derive analytical results
for some particular types of noises and interpret them in the framework of
on-off intermittency. Besides, we perform a cumulant expansion for a random
noise with arbitrary power spectrum density and show that the intermittent
regime is controlled by the ratio between the departure from the threshold and
the value of the PSD of the noise at zero frequency. Our results are in
agreement with numerical simulations performed with two types of random
perturbations: colored Gaussian noise and deterministic fluctuations of a
chaotic variable. Extensions of this study to another, more complex, system are
presented and the underlying mechanisms are discussed.Comment: 13pages, 13 figure
Observation of resonant interactions among surface gravity waves
We experimentally study resonant interactions of oblique surface gravity
waves in a large basin. Our results strongly extend previous experimental
results performed mainly for perpendicular or collinear wave trains. We
generate two oblique waves crossing at an acute angle, while we control their
frequency ratio, steepnesses and directions. These mother waves mutually
interact and give birth to a resonant wave whose properties (growth rate,
resonant response curve and phase locking) are fully characterized. All our
experimental results are found in good quantitative agreement with four-wave
interaction theory with no fitting parameter. Off-resonance experiments are
also reported and the relevant theoretical analysis is conducted and validated.Comment: 11 pages, 7 figure
Critical exponents in zero dimensions
In the vicinity of the onset of an instability, we investigate the effect of
colored multiplicative noise on the scaling of the moments of the unstable mode
amplitude. We introduce a family of zero dimensional models for which we can
calculate the exact value of the critical exponents for all the
moments. The results are obtained through asymptotic expansions that use the
distance to onset as a small parameter. The examined family displays a variety
of behaviors of the critical exponents that includes anomalous exponents:
exponents that differ from the deterministic (mean-field) prediction, and
multiscaling: non-linear dependence of the exponents on the order of the
moment
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