117 research outputs found
Global vs local energy dissipation: the energy cycle of the turbulent von K\'arm\'an flow
In this paper, we investigate the relations between global and local energy
transfers in a turbulent von K\'arm\'an flow. The goal is to understand how and
where energy is dissipated in such a flow and to reconstruct the energy cycle
in an experimental device where local as well as global quantities can be
measured. We use PIV measurements and we model the Reynolds stress tensor to
take subgrid scales into account. This procedure involves a free parameter that
is calibrated using angular momentum balance. We then estimate the local and
global mean injected and dissipated power for several types of impellers, for
various Reynolds numbers and for various flow topologies. These PIV estimates
are then compared with direct injected power estimates provided by torque
measurements at the impellers. The agreement between PIV estimates and direct
measurements depends on the flow topology. In symmetric situations, we are able
to capture up to 90% of the actual global energy dissipation rate. However, our
results become increasingly inaccurate as the shear layer responsible for most
of the dissipation approaches one of the impellers, and cannot be resolved by
our PIV set-up. Finally, we show that a very good agreement between PIV
estimates and direct measurements is obtained using a new method based on the
work of Duchon and Robert which generalizes the K\'arm\'an-Howarth equation to
nonisotropic, nonhomogeneous flows. This method provides parameter-free
estimates of the energy dissipation rate as long as the smallest resolved scale
lies in the inertial range. These results are used to evidence a well-defined
stationary energy cycle within the flow in which most of the energy is injected
at the top and bottom impellers, and dissipated within the shear layer. The
influence of the mean flow geometry and the Reynolds number on this energy
cycle is studied for a wide range of parameters
Wave turbulence description of interacting particles: Klein-Gordon model with a Mexican-hat potential
In field theory, particles are waves or excitations that propagate on the
fundamental state. In experiments or cosmological models one typically wants to
compute the out-of-equilibrium evolution of a given initial distribution of
such waves. Wave Turbulence deals with out-of-equilibrium ensembles of weakly
nonlinear waves, and is therefore well-suited to address this problem. As an
example, we consider the complex Klein-Gordon equation with a Mexican-hat
potential. This simple equation displays two kinds of excitations around the
fundamental state: massive particles and massless Goldstone bosons. The former
are waves with a nonzero frequency for vanishing wavenumber, whereas the latter
obey an acoustic dispersion relation. Using wave turbulence theory, we derive
wave kinetic equations that govern the coupled evolution of the spectra of
massive and massless waves. We first consider the thermodynamic solutions to
these equations and study the wave condensation transition, which is the
classical equivalent of Bose-Einstein condensation. We then focus on nonlocal
interactions in wavenumber space: we study the decay of an ensemble massive
particles into massless ones. Under rather general conditions, these massless
particles accumulate at low wavenumber. We study the dynamics of waves
coexisting with such a strong condensate, and we compute rigorously a nonlocal
Kolmogorov-Zakharov solution, where particles are transferred non-locally to
the condensate, while energy cascades towards large wave numbers through local
interactions. This nonlocal cascading state constitute the intermediate
asymptotics between the initial distribution of waves and the thermodynamic
state reached in the long-time limit
Intermittency in the homopolar disk-dynamo
We study a modified Bullard dynamo and show that this system is equivalent to
a nonlinear oscillator subject to a multiplicative noise. The stability
analysis of this oscillator is performed. Two bifurcations are identified,
first towards an `` intermittent\rq\rq state where the absorbing (non-dynamo)
state is no more stable but the most probable value of the amplitude of the
oscillator is still zero and secondly towards a `` turbulent\rq\rq (dynamo)
state where it is possible to define unambiguously a (non-zero) most probable
value around which the amplitude of the oscillator fluctuates. The bifurcation
diagram of this system exhibits three regions which are analytically
characterized
Entropy production and multiple equilibria: the case of the ice-albedo feedback
Nonlinear feedbacks in the Earth System provide mechanisms that can prove
very useful in understanding complex dynamics with relatively simple concepts.
For example, the temperature and the ice cover of the planet are linked in a
positive feedback which gives birth to multiple equilibria for some values of
the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate
unstable solution. In this study, we show an analogy between a classical
dynamical system approach to this problem and a Maximum Entropy Production
(MEP) principle view, and we suggest a glimpse on how to reconcile MEP with the
time evolution of a variable. It enables us in particular to resolve the
question of the stability of the entropy production maxima. We also compare the
surface heat flux obtained with MEP and with the bulk-aerodynamic formula.Comment: 29 pages, 12 figure
A zero-mode mechanism for spontaneous symmetry breaking in a turbulent von K\'arm\'an flow
We suggest that the dynamical spontaneous symmetry breaking reported in a
turbulent swirling flow at by Cortet et al., Phys. Rev. Lett., 105,
214501 (2010) can be described through a continuous one parameter family
transformation (amounting to a phase shift) of steady states and could be the
analogue of the Goldstone mode of the vertical translational symmetry in an
ideal system. We investigate a possible mechanism of emergence of such
spontaneous symmetry breaking in a toy model of our out-equilibrium system,
derived from its equilibrium counterpart. We show that the stationary states
are solution of a linear differential equation. For a specific value of the
Reynolds number, they are subject to a spontaneous symmetry breaking through a
zero-mode mechanism. These zero-modes obey a Beltrami property and their
spontaneous fluctuations can be seen as the "phonon of turbulence".Comment: 17 pages, 4 figures, submitted to New. J. Phy
Three-dimensional magnetic field reconstruction in the VKS experiment through Galerkin transforms
International audienceWe present a method for three-dimensional (3D) magnetic field reconstruction based on Galerkin transforms. We test it over synthetic fields and real solenoidal (velocity) fields, measured in a water experiment. Our study shows that reliable reconstructions are possible provided that the probes are sufficiently sampled and located in shifted configurations. A preliminary application of our method is performed on results obtained in the VKS dynamo experiment (Bourgoin et al 2002 Phys. Fluids 14 3046). We show that the stationary dynamos obtained with counter-rotating impellers are mainly axisymmetric, with a non-axisymmetric part that decreases with increasing Reynolds numbers. Most of the azimuthal energy is localized near the (iron) impellers, confirming their importance in the dynamo process
Statistical early-warning indicators based on Auto-Regressive Moving-Average processes
We address the problem of defining early warning indicators of critical
transition. To this purpose, we fit the relevant time series through a class of
linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We
define two indicators representing the total order and the total persistence of
the process, linked, respectively, to the shape and to the characteristic decay
time of the autocorrelation function of the process. We successfully test the
method to detect transitions in a Langevin model and a 2D Ising model with
nearest-neighbour interaction. We then apply the method to complex systems,
namely for dynamo thresholds and financial crisis detection.Comment: 5 pages, 4 figure
Eckhaus-like instability of large scale coherent structures in a fully turbulent von K\'arm\'an flow
The notion of instability of a turbulent flow is introduced in the case of a
von K\'arm\'an flow thanks to the monitoring of the spatio-temporal spectrum of
the velocity fluctuations, combined with projection onto suitable Beltrami
modes. It is shown that the large scale coherent fluctuations of the flow obeys
a sequence of Eckhaus instabilities when the Reynolds number is
varied from to . This sequence results in modulations of
increasing azimuthal wavenumber. The basic state is the laminar or
time-averaged flow at an arbitrary , which is axi-symmetric, i.e.
with a azimuthal wavenumber. Increasing leads to
non-axisymmetric modulations with increasing azimuthal wavenumber from to
. These modulations are found to rotate in the azimuthal direction. However
no clear rotation frequency can be established until . Above, they become periodic with an increasing frequency. We
finally show that these modulations are connected with the coherent structures
of the mixing shear layer. The implication of these findings for the turbulence
parametrization is discussed. Especially, they may explain why simple eddy
viscosity models are able to capture complex turbulent flow dynamics
Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere
The large-scale circulation of planetary atmospheres like that of the Earth
is traditionally thought of in a dynamical framework. Here, we apply the
statistical mechanics theory of turbulent flows to a simplified model of the
global atmosphere, the quasi-geostrophic model, leading to non-trivial
equilibria. Depending on a few global parameters, the structure of the flow may
be either a solid-body rotation (zonal flow) or a dipole. A second order phase
transition occurs between these two phases, with associated spontaneous
symmetry-breaking in the dipole phase. This model allows us to go beyond the
general theory of marginal ensemble equivalence through the notion of Goldstone
modes.Comment: 7 pages, 3 figures; accepted for publication in Physical Review
Kinematic Alpha Tensors and dynamo mechanisms in a von Karman swirling flow
We provide experimental and numerical evidence of in-blades vortices in the von Karman swirling flow. We estimate the associated kinematic α-effect tensor and show that it is compatible with recent models of the von Karman Sodium (VKS) dynamo. We further show that depending on the relative frequency of the two impellers, the dominant dynamo mechanism may switch from α^2 to α − Ω dynamo. We discuss some implications of these results for VKS experiments
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