Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid

We analyze theoretically and experimentally the far-field viscous decay of a two-dimensional inertial wave beam emitted by a harmonic line source in a rotating fluid. By identifying the relevant conserved quantities along the wave beam, we show how the beam structure and decay exponent are governed by the multipole order of the source. Two wavemakers are considered experimentally, a pulsating and an oscillating cylinder, aiming to produce a monopole and a dipole source, respectively. The relevant conserved quantity which discriminates between these two sources is the instantaneous flowrate along the wave beam, which is non-zero for the monopole and zero for the dipole. For each source the beam structure and decay exponent, measured using particle image velocimetry, are in good agreement with the predictions

Disentangling inertial waves from eddy turbulence in a forced rotating turbulence experiment

We present a spatio-temporal analysis of a statistically stationary rotating turbulence experiment, aiming to extract a signature of inertial waves, and to determine the scales and frequencies at which they can be detected. The analysis uses two-point spatial correlations of the temporal Fourier transform of velocity fields obtained from time-resolved stereoscopic particle image velocimetry measurements in the rotating frame. We quantify the degree of anisotropy of turbulence as a function of frequency and spatial scale. We show that this space-time-dependent anisotropy is well described by the dispersion relation of linear inertial waves at large scale, while smaller scales are dominated by the sweeping of the waves by fluid motion at larger scales. This sweeping effect is mostly due to the low-frequency quasi-two-dimensional component of the turbulent flow, a prominent feature of our experiment which is not accounted for by wave turbulence theory. These results question the relevance of this theory for rotating turbulence at the moderate Rossby numbers accessible in laboratory experiments, which are relevant to most geophysical and astrophysical flows

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

Strong dynamical effects during stick-slip adhesive peeling

We consider the classical problem of the stick-slip dynamics observed when peeling a roller adhesive tape at a constant velocity. From fast imaging recordings, we extract the dependencies of the stick and slip phases durations with the imposed peeling velocity and peeled ribbon length. Predictions of Maugis and Barquins [in Adhesion 12, edited by K.W. Allen, Elsevier ASP, London, 1988, pp. 205--222] based on a quasistatic assumption succeed to describe quantitatively our measurements of the stick phase duration. Such model however fails to predict the full stick-slip cycle duration, revealing strong dynamical effects during the slip phase.Comment: Soft Matter 201

Experimental study of the effect of disorder on subcritical crack growth dynamics

The growth dynamics of a single crack in a heterogeneous material under subcritical loading is an intermittent process; and many features of this dynamics have been shown to agree with simple models of thermally activated rupture. In order to better understand the role of material heterogeneities in this process, we study the subcritical propagation of a crack in a sheet of paper in the presence of a distribution of small defects such as holes. The experimental data obtained for two different distributions of holes are discussed in the light of models that predict the slowing down of crack growth when the disorder in the material is increased; however, in contradiction with these theoretical predictions, the experiments result in longer lasting cracks in a more ordered scenario. We argue that this effect is specific to subcritical crack dynamics and that the weakest zones between holes at close distance to each other are responsible both for the acceleration of the crack dynamics and the slightly different roughness of the crack path.Comment: 4 pages, 5 figures, accepted in Physical Review Letters (http://prl.aps.org

Multiscale Stick-Slip Dynamics of Adhesive Tape Peeling

Using a high-speed camera, we follow the propagation of the detachment front during the peeling of an adhesive tape from a flat surface. In a given range of peeling velocity, this front displays a multiscale unstable dynamics, entangling two well-separated spatiotemporal scales, which correspond to microscopic and macroscopic dynamical stick-slip instabilities. While the periodic release of the stretch energy of the whole peeled ribbon drives the classical macro-stick-slip, we show that the micro-stick-slip, due to the regular propagation of transverse dynamic fractures discovered by Thoroddsen et al. [Phys. Rev. E 82, 046107 (2010)], is related to a high-frequency periodic release of the elastic bending energy of the adhesive ribbon concentrated in the vicinity of the peeling front.Comment: to appear in Physical Review Letters (2015

Relevance of visco-plastic theory in a multi-directional inhomogeneous granular flow

We confront a recent visco-plastic description of dense granular flows [P. Jop et al, Nature, {\bf 441} (2006) 727] with multi-directional inhomogeneous steady flows observed in non-smooth contact dynamics simulations of 2D half-filled rotating drums. Special attention is paid to check separately the two underlying fundamental statements into which the considered theory can be recast, namely (i) a single relation between the invariants of stress and strain rate tensors and (ii) the alignment between these tensors. Interestingly, the first prediction is fairly well verified over more than four decades of small strain rate, from the surface rapid flow to the quasi-static creep phase, where it is usually believed to fail because of jamming. On the other hand, the alignment between stress and strain rate tensors is shown to fail over the whole flow, what yields an apparent violation of the visco-plastic rheology when applied without care. In the quasi-static phase, the particularly large misalignment is conjectured to be related to transient dilatancy effects