Probing an nonequilibrium Einstein relation in an aging colloidal glass

We present a direct experimental measurement of an effective temperature in a colloidal glass of Laponite, using a micrometric bead as a thermometer. The nonequilibrium fluctuation-dissipation relation, in the particular form of a modified Einstein relation, is investigated with diffusion and mobility measurements of the bead embedded in the glass. We observe an unusual non-monotonic behavior of the effective temperature : starting from the bath temperature, it is found to increase up to a maximum value, and then decreases back, as the system ages. We show that the observed deviation from the Einstein relation is related to the relaxation times previously measured in dynamic light scattering experiments.Comment: 4 pages, 4 figures, corrected references, published in Phys. Rev. Lette

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 $Re=40~000$ 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

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 $\mathrm{Re}$ is varied from $10^2$ to $10^6$. This sequence results in modulations of increasing azimuthal wavenumber. The basic state is the laminar or time-averaged flow at an arbitrary $\mathrm{Re}$, which is axi-symmetric, i.e. with a $0$ azimuthal wavenumber. Increasing $\mathrm{Re}$ leads to non-axisymmetric modulations with increasing azimuthal wavenumber from $1$ to $3$. These modulations are found to rotate in the azimuthal direction. However no clear rotation frequency can be established until $\mathrm{Re}\approx 4\times 10^3$. 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

Rotational microrheology of Maxwell fluids using micron-sized wires

We demonstrate a simple method for rotational microrheology in complex fluids, using micrometric wires. The three-dimensional rotational Brownian motion of the wires suspended in Maxwell fluids is measured from their projection on the focal plane of a microscope. We analyze the mean-squared angular displacement of the wires of length between 1 and 40 microns. The viscoelastic properties of the suspending fluids are extracted from this analysis and found to be in good agreement with macrorheology data. Viscosities of simple and complex fluids between 0.01 and 30 Pa.s could be measured. As for the elastic modulus, values up to ~ 5 Pa could be determined. This simple technique, allowing for a broad range of probed length scales, opens new perspectives in microrheology of heterogeneous materials such as gels, glasses and cells.Comment: to appear in Soft Matte

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

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 $\Upsilon$ 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 $\Upsilon$ 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 $\Upsilon$ 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

On the analysis of Rayleigh-B\'enard convection using Latent Dirichlet Allocation

We apply a probabilistic clustering method, Latent Dirichlet Allocation (LDA), to characterize the largescale dynamics of Rayleigh-B\'enard convection. The method, introduced in Frihat et al. 2021, is applied to a collection of snapshots in the vertical mid-planes of a cubic cell for Rayleigh numbers in the range [106, 108]. For the convective heat flux, temperature and kinetic energy, the decomposition identifies latent factors, called motifs, which consist of connex regions of fluid. Each snapshot is modelled with a sparse combination of motifs, the coefficients of which are called the weights. The spatial extent of the motifs varies across the cell and with the Rayleigh number. We show that the method is able to provide a compact representation of the heat flux and displays good generative properties. At all Rayleigh numbers the dominant heat flux motifs consist of elongated structures located mostly within the vertical boundary layer, at a quarter of the cavity height. Their weights depend on the orientation of the large-scale circulation (LSC). A simple model relating the conditionally averaged weight of the motifs to the relative strength of the corner rolls and of the large-scale circulation, is found to predict well the average LSC reorientation rate. Application of LDA to the temperature fluctuations shows that temperature motifs are well correlated with heat flux motifs in space as well as in time, and to some lesser extent with kinetic energy motifs. The abrupt decrease of the reorientation rate observed at 108 is associated with a strong concentration of plumes impinging layers onto the corners of the cell, which decrease the temperature difference within the corner structures. It is also associated with a reinforcement of the longitudinal wind through formation and entrainment of new plumes.Comment: 42 page

Euler-like modelling of dense granular flows: application to a rotating drum

General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be encoded in two scalar functions only. We checked such prediction on steady surface flows in a rotating drum simulated through the Non-Smooth Contact Dynamics method. This result is non trivial because granular flows are dissipative and therefore not necessarily compatible with Euler equation. Finally, we briefly discuss some possible ways to predict theoretically these two functions using statistical mechanics