104 research outputs found
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
Sensitivity of convective structures to mean flow boundary conditions: A correlation between symmetry and dynamics
International audienceVarious simple structures have been proposed for modeling the transition to time dependence of convective patterns in extended geometries. In order to further question their relevance to the dynamics of complex structures ͑textures͒, we introduce a change of boundary conditions from both an experimental and a theoretical side. It consists in keeping the same roll structure but in separating the boundaries of the mean flows from those of the roll flows. This induces negligible effects on symmetric structures ͑straight rolls and foci͒ but dramatic changes on asymmetric ones ͑focus pairs and textures͒, especially regarding the onset of time dependence. Both kinds of sensitivity to this change of boundary conditions are recovered from the Cross-Newell equations. They reveal a correlation between symmetry and dynamics that prevents symmetric structures from modeling asymmetric ones. On the opposite side, they point to focus pairs as a plausible prototype of the mechanisms of time-dependence at work in textures
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
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
Probing turbulence intermittency via Auto-Regressive Moving-Average models
We suggest a new approach to probing intermittency corrections to the
Kolmogorov law in turbulent flows based on the Auto-Regressive Moving-Average
modeling of turbulent time series. We introduce a new index that
measures the distance from a Kolmogorov-Obukhov model in the Auto-Regressive
Moving-Average models space. Applying our analysis to Particle Image
Velocimetry and Laser Doppler Velocimetry measurements in a von K\'arm\'an
swirling flow, we show that is proportional to the traditional
intermittency correction computed from the structure function. Therefore it
provides the same information, using much shorter time series. We conclude that
is a suitable index to reconstruct the spatial intermittency of the
dissipation in both numerical and experimental turbulent fields.Comment: 5 page
Evidence for Forcing-Dependent Steady States in a Turbulent Swirling Flow
We study the influence on steady turbulent states of the forcing in a von Karman flow, at constant impeller speed, or at constant torque. We find that the different forcing conditions change the nature of the stability of the steady states and reveal dynamical regimes that bear similarities to low-dimensional systems. We suggest that this forcing dependence may be applicable to other turbulent systems
A statistical mechanics framework for the large-scale structure of turbulent von K{\'a}rm{\'a}n flows
In the present paper, recent experimental results on large scale coherent
steady states observed in experimental von K{\'a}rm{\'a}n flows are revisited
from a statistical mechanics perspective. The latter is rooted on two levels of
description. We first argue that the coherent steady states may be described as
the equilibrium states of well-chosen lattice models, that can be used to
define global properties of von K{\'a}rm{\'a}n flows, such as their
temperatures. The equilibrium description is then enlarged, in order to
reinterpret a series of results about the stability of those steady states,
their susceptibility to symmetry breaking, in the light of a deep analogy with
the statistical theory of Ferromagnetism. We call this analogy
"Ferro-Turbulence
Travelling and Standing Waves in a Spatially Forced 2D Convection Experiment
International audienceRayleigh-Bénard convection is studied in a rectangular geometry with a spatial forcing induced in one direction by electric wires. When using fluids of relatively large Prandtl numbers, this forcing allows the existence of a perfect one-dimensional pattern until the onset of bimodal convection. The transition to bidimensional convection is studied for increasing Rayleigh number and reveals the existence of different spatio-temporal regimes depending on the value of the forcing. At the onset of the transition, a stationary pattern is observed for weak forcing, while travelling waves are evidenced for strong forcing. Both behaviours give place to collective oscillations at higher Rayleigh number
Origin of waves in surface-tension-driven convection
International audienceWaves appear in a liquid layer with a free surface if a sufficiently high horizontal temperature gradient is imposed. These waves have been compared to the hydrothermal waves predicted by a linear stability analysis of a parallel flow. However, depending on the experimental configurations, significant differences with theory are found. We show that there exists another kind of wave that cannot be explained by previous analysis. Our aim is to investigate which is the mechanism leading to this instability. Differential interferometry is used to obtain quantitative information on the temperature field. Experimental evidence is presented suggesting that these waves are the result of a boundary layer instability: the roll near the hot wall begins to oscillate, and the perturbations are dragged and amplified downflow. This mechanism could explain discrepancies between theory and some experimental observations
Supercritical Eckhaus Instability for Surface-Tension-Driven Hydrothermal Waves
International audienceWe study the nonlinear dynamics of hydrothermal waves produced by a surface-tension-driven convective flow in a long and thin annular channel heated from the side. Above onset, the supercritical traveling wave pattern undergoes a secondary instability: a supercritical Eckhaus instability. This leads to a small-wave-number phase-modulated nonlinear mode, and shows the first experimental evidence of a nonlinearly saturated phase instability mode for traveling wave patterns. At higher forcing level, this secondary pattern is subject to a tertiary instability. This mode is an amplitude mode characterized by traveling hole patterns, i.e., space-time defects that change the wave numbe
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