234 research outputs found
Fourier analysis of wave turbulence in a thin elastic plate
The spatio-temporal dynamics of the deformation of a vibrated plate is
measured by a high speed Fourier transform profilometry technique. The
space-time Fourier spectrum is analyzed. It displays a behavior consistent with
the premises of the Weak Turbulence theory. A isotropic continuous spectrum of
waves is excited with a non linear dispersion relation slightly shifted from
the linear dispersion relation. The spectral width of the dispersion relation
is also measured. The non linearity of this system is weak as expected from the
theory. Finite size effects are discussed. Despite a qualitative agreement with
the theory, a quantitative mismatch is observed which origin may be due to the
dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov
casade.Comment: accepted for publication in European Physical Journal B see
http://www.epj.or
Acceleration and vortex filaments in turbulence
We report recent results from a high resolution numerical study of fluid
particles transported by a fully developed turbulent flow. Single particle
trajectories were followed for a time range spanning more than three decades,
from less than a tenth of the Kolmogorov time-scale up to one large-eddy
turnover time. We present some results concerning acceleration statistics and
the statistics of trapping by vortex filaments.Comment: 10 pages, 5 figure
Are there waves in elastic wave turbulence ?
An thin elastic steel plate is excited with a vibrator and its local velocity
displays a turbulent-like Fourier spectrum. This system is believed to develop
elastic wave turbulence. We analyze here the motion of the plate with a
two-point measurement in order to check, in our real system, a few hypotheses
required for the Zakharov theory of weak turbulence to apply. We show that the
motion of the plate is indeed a superposition of bending waves following the
theoretical dispersion relation of the linear wave equation. The nonlinearities
seem to efficiently break the coherence of the waves so that no modal structure
is observed. Several hypotheses of the weak turbulence theory seem to be
verified, but nevertheless the theoretical predictions for the wave spectrum
are not verified experimentally.Comment: published in Physical Review Letters volume 100, 234505 (2008)
http://link.aps.org/abstract/PRL/v100/e234505 minor modification
Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation
We use the multifractal formalism to describe the effects of dissipation on
Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds
number experiments and direct numerical simulation (DNS) data. We show that
this approach reproduces the shape evolution of velocity increment probability
density functions (PDF) from Gaussian to stretched exponentials as the time lag
decreases from integral to dissipative time scales. A quantitative
understanding of the departure from scaling exhibited by the magnitude
cumulants, early in the inertial range, is obtained with a free parameter
function D(h) which plays the role of the singularity spectrum in the
asymptotic limit of infinite Reynolds number. We observe that numerical and
experimental data are accurately described by a unique quadratic D(h) spectrum
which is found to extend from to , as
the signature of the highly intermittent nature of Lagrangian velocity
fluctuations.Comment: 5 pages, 3 figures, to appear in PR
Lagrangian stochastic modelling of acceleration in turbulent wall-bounded flows
The Lagrangian approach is natural for studying issues of turbulent dispersion and mixing. We propose in this work a general Lagrangian stochastic model for inhomogeneous turbulent flows, using velocity and acceleration as dynamical variables. The model takes the form of a diffusion process, and the coefficients of the model are determined via Kolmogorov theory and the requirement of consistency with velocity-based models. We show that this model generalises both the acceleration-based models for homogeneous flows as well as velocity-based generalised Langevin models. The resulting closed model is applied to a channel flow at high Reynolds number, and compared to experiments as well as direct numerical simulations. A hybrid approach coupling the stochastic model with a Reynolds-averaged Navier-Stokes model is used to obtain a self-consistent model, as is commonly used in probability density function methods. Results highlight that most of the acceleration features are well represented, notably the anisotropy between streamwise and wall-normal components and the strong intermittency. These results are valuable, since the model improves on velocity-based models for boundary layers while remaining relatively simple. Our model also sheds some light on the statistical mechanisms at play in the near-wall region
Measurement of Lagrangian velocity in fully developed turbulence
We have developed a new experimental technique to measure the Lagrangian
velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler
tracking. This method yields a direct access to the velocity of a single
particule at a turbulent Reynolds number . Its dynamics is
analyzed with two decades of time resolution, below the Lagrangian correlation
time. We observe that the Lagrangian velocity spectrum has a Lorentzian form
, in agreement
with a Kolmogorov-like scaling in the inertial range. The probability density
function (PDF) of the velocity time increments displays a change of shape from
quasi-Gaussian a integral time scale to stretched exponential tails at the
smallest time increments. This intermittency, when measured from relative
scaling exponents of structure functions, is more pronounced than in the
Eulerian framework.Comment: 4 pages, 5 figures. to appear in PR
Long time correlations in Lagrangian dynamics: a key to intermittency in turbulence
New aspects of turbulence are uncovered if one considers flow motion from the
perspective of a fluid particle (known as the Lagrangian approach) rather than
in terms of a velocity field (the Eulerian viewpoint). Using a new experimental
technique, based on the scattering of ultrasounds, we have obtained a direct
measurement of particle velocities, resolved at all scales, in a fully
turbulent flow. It enables us to approach intermittency in turbulence from a
dynamical point of view and to analyze the Lagrangian velocity fluctuations in
the framework of random walks. We find experimentally that the elementary steps
in the 'walk' have random uncorrelated directions but a magnitude that is
extremely long-range correlated in time. Theoretically, we study a Langevin
equation that incorporates these features and we show that the resulting
dynamics accounts for the observed one- and two-point statistical properties of
the Lagrangian velocity fluctuations. Our approach connects the intermittent
statistical nature of turbulence to the dynamics of the flow.Comment: 4 pages, 4 figure
Investigation of a generalized Obukhov Model for Turbulence
We introduce a generalization of Obukhov's model [A.M. Obukhov, Adv. Geophys.
6, 113 (1959)] for the description of the joint position-velocity statistics of
a single fluid particle in fully developed turbulence. In the presented model
the velocity is assumed to undergo a continuous time random walk. This takes
into account long time correlations. As a consequence the evolution equation
for the joint position-velocity probability distribution is a Fokker-Planck
equation with a fractional time derivative. We determine the solution of this
equation in the form of an integral transform and derive a relation for
arbitrary single time moments. Analytical solutions for the joint probability
distribution and its moments are given.Comment: 10 page
Magnetic field reversals in an experimental turbulent dynamo
We report the first experimental observation of reversals of a dynamo field
generated in a laboratory experiment based on a turbulent flow of liquid
sodium. The magnetic field randomly switches between two symmetric solutions B
and -B. We observe a hierarchy of time scales similar to the Earth's magnetic
field: the duration of the steady phases is widely distributed, but is always
much longer than the time needed to switch polarity. In addition to reversals
we report excursions. Both coincide with minima of the mechanical power driving
the flow. Small changes in the flow driving parameters also reveal a large
variety of dynamo regimes.Comment: 5 pages, 4 figure
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