Frédéric Moisy

Geometry and clustering of intense structures in isotropic turbulence

The regions associated with high levels of vorticity and energy dissipation are studied in numerically simulated isotropic turbulence at Re λ = 168. Their geometry and spatial distribution are characterized by means of box-counting methods. No clear scaling is observed for the box counts of intense strain rate and vorticity sets, presumably due to the limited inertial range, but it is shown that, even in that case, the box-counting method can be refined to characterize the shape of the intense structures themselves, as well as their spatial distribution. The fractal dimension of the individual vorticity structures, D ω → 1.1 ± 0.1, suggests that they tend to form filamentary vortices in the limit of high vorticity threshold. On the other hand, the intense dissipation structures have dimensions D s ≃ 1.7 ± 0.1, with no noticeable dependence on the threshold, suggesting structures in the form of sheets or ribbons. Statistics of the associated aspect ratios for different thresholds support these observations. Finally box counting is used to characterize the spatial distribution of the baricentres of the structures

Decaying grid-generated turbulence in a rotating tank

The decay of initially three-dimensional homogeneous turbulence in a rotating frame is experimentally investigated. Turbulence is generated by rapidly towing a grid in a rotating water tank, and the velocity field in a plane perpendicular to the rotation axis is measured by means of particle image velocimetry. During the decay, strong cyclonic coherent vortices emerge, as the result of enhanced stretching of the cyclonic vorticity by the background rotation, and the selective instability of the anticyclonic vorticity by the Coriolis force. This asymmetry towards cyclonic vorticity grows on a time scale Ω−1 (Ω is the rotation rate), until the friction from the Ekman layers becomes dominant. The energy spectrum perpendicular to the rotation axis becomes steeper as the instantaneous Rossby number Roω=ω′∕2Ω decreases below the value 2±0.5 (ω′ is the root-mean square of the vertical vorticity). The spectral exponent increases in time from its classical Kolmogorov value 5∕3 up to values larger than 2. Below the...

Ship Wakes: Kelvin or Mach Angle?

From the analysis of a set of airborne images of ship wakes, we show that the wake angles decrease as U(-1) at large velocities, in a way similar to the Mach cone for supersonic airplanes. This previously unnoticed Mach-like regime is in contradiction with the celebrated Kelvin prediction of a constant angle of 19.47° independent of the ships speed. We propose here a model, confirmed by numerical simulations, in which the finite size of the disturbance explains this transition between the Kelvin and Mach regimes at a Froude number Fr=U/√[gL]~/=0.5, where L is the hull ship length.

Instabilities in the flow between co- and counter-rotating disks

The flow between two rotating disks (radius to heigh ratio of 20.9), enclosed by a rotating cylinder, is investigated experimentally in the cases of both co- and counter-rotation. This flow gives rise to a large gallery of instability patterns. A regime diagram of these patterns is presented in the ( Re b , Re t )-plane, where Re b,t is the Reynolds number associated with each disk. The co-rotation case and the weak counter-rotation case are very similar to the rotor–stator case, both for the basic flow and the instability patterns: the basic flow consists of two boundary layers near each disk and the instability patterns are the axisymmetric vortices and the positive spirals described in the rotor–stator experiments of Gauthier, Gondret & Rabaud (1999), Schouveiler, Le Gal & Chauve (2001), and the numerical study of Serre, Crespo del Arco & Bontoux (2001). The counter-rotation case with higher rotation ratio is more complex: above a given rotation ratio, the recirculation flow becomes organized into a two-cell structure with the appearance of a stagnation circle on the slower disk. A new kind of instability pattern is observed, called negative spirals. Measurements of the main characteristics of this pattern are presented, including growth times, critical modes and phase velocities.

Experimental and numerical study of the shear layer instability between two counter-rotating disks

The shear layer instability in the flow between two counter-rotating disks enclosed by a cylinder is investigated experimentally and numerically, for radius-to-height ratio Γ=R/h between 2 and 21. For sufficiently large rotation ratio, the internal shear layer that separates two regions of opposite azimuthal velocities is prone to an azimuthal symmetry breaking, which is investigated experimentally by means of visualization and particle image velocimetry. The associated pattern is a combination of a sharp-cornered polygonal pattern, as observed by Lopez et al. (2002) for low aspect ratio, surrounded by a set of spiral arms, first described by Gauthier et al. (2002) for high aspect ratio. The spiral arms result from the interaction of the shear layer instability with the Ekman boundary layer over the faster rotating disk. Stability curves and critical modes are experimentally measured for the whole range of aspect ratios, and are found to compare well with numerical simulations of the three-dimensional time-dependent Navier–Stokes equations over an extensive range of parameters. Measurements of a local Reynolds number based on the shear layer thickness confirm that a shear layer instability, with only weak curvature effect, is responsible for the observed patterns. This scenario is supported by the observed onset modes, which scale as the shear layer radius, and by the measured phase velocities.

Energy decay of rotating turbulence with confinement effects

The energy decay of grid-generated turbulence in a rotating tank is experimentally investigated by means of particle image velocimetry. For times smaller than the Ekman time scale, a range of approximate self-similar decay is found, in the form u2(t)∝t−n, with the exponent n decreasing from 2 to values close to 1 as the rotation rate is increased. Even at very weak rotation rates, rotation is shown to have a strong indirect influence on the decay law, by making the integral length scale to quickly saturate to the experiment size through the propagation of inertial waves. The experimental decay exponents are found in good agreement with the predicted values from a phenomenological model based on the exponent of the energy spectrum, in which both the effects of the rotation and the confinement are taken into account.

Direct measurements of anisotropic energy transfers in a rotating turbulence experiment.

We investigate experimentally the influence of a background rotation on the energy transfers in decaying grid turbulence. The anisotropic energy flux density F(r) = , where δu is the vector velocity increment over separation r, is determined for the first time by using particle image velocimetry. We show that rotation induces an anisotropy of the energy flux ∇·F, which leads to an anisotropy growth of the energy distribution E(r) = <(δu)²>, in agreement with the von Kármán-Howarth-Monin equation. Surprisingly, our results prove that this anisotropy growth is essentially driven by a nearly radial, but orientation-dependent, energy flux density F(r).

Using cavitation to measure statistics of low-pressure events in large-Reynolds-number turbulence

No completely satisfactory experimental technique exists for making noninvasive measurements of the pressure field in a turbulent flow. Conventional pressure sensors are typically unable to resolve the finest scales of intense turbulence. More fundamentally, conventional sensors usually measure the pressure on the wall of the container rather than in the bulk of the flow. Pressure probes can be constructed which extend into the flow and measure the pressure at a point, but these can perturb the flow and usually suffer from velocity contamination. In this paper, we report studies using cavitation to detect large negative pressure fluctuations in a turbulent water flow between counter-rotating disks. The large-Reynolds-number water flow is seeded with small gas bubbles and the hydrostatic pressure is adjusted so that negative pressure fluctuations go below the vapor pressure and trigger cavitation. The seed bubbles are a negligible perturbation to the system up until the moment that cavitation is triggered. The spatial and temporal resolution of the measurement is very high, and is set by the size, number density, and resonant frequencies of the seed bubbles. We use high-speed video imaging of the coherent pressure structures marked by cavitation as a way to visualize the low-pressure filaments. In addition, we study the probability distribution of large negative pressure fluctuations by measuring the light scattered from cavitating bubbles in a small region of the flow. From this we estimate the scaling with Reynolds number of the negative tail of the pressure distribution. The importance of the pressure in the equations of fluid motion has motivated many studies of the properties of the pressure field. 1‐4 Numerical simulations 5‐9 and experimental measurements from conventional pressure probes 10‐12 have found that the pressure distribution is skewed to negative pressures where there is an exponential tail. It has been shown analytically 13 that this does not necessarily indicate the presence of structures in the flow because even Gaussian velocity fields produce exponential pressure tails. However, a careful numerical study 7 finds that despite qualitative

Direct and inverse energy cascades in a forced rotating turbulence experiment

We present experimental evidence for a double cascade of kinetic energy in a statistically stationary rotating turbulence experiment. Turbulence is generated by a set of vertical flaps, which continuously injects velocity fluctuations towards the center of a rotating water tank. The energy transfers are evaluated from two-point third-order three-component velocity structure functions, which we measure using stereoscopic particle image velocimetry in the rotating frame. Without global rotation, the energy is transferred from large to small scales, as in classical three-dimensional turbulence. For nonzero rotation rates, the horizontal kinetic energy presents a double cascade: a direct cascade at small horizontal scales and an inverse cascade at large horizontal scales. By contrast, the vertical kinetic energy is always transferred from large to small horizontal scales, a behavior reminiscent of the dynamics of a passive scalar in two-dimensional turbulence. At the largest rotation rate, the flow is nearly two-dimensional, and a pure inverse energy cascade is found for the horizontal energy. To describe the scale-by-scale energy budget, we consider a generalization of the Karman-Howarth-Monin equation to inhomogeneous turbulent flows, in which the energy input is explicitly described as the advection of turbulent energy from the flaps through the surface of the control volume where the measurements are performed.

Mach-like capillary-gravity wakes.

We determine experimentally the angle α of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity U for Bond numbers Bo(D)=D/λ(c) ranging between 0.1 and 4.2, where D is the cylinder diameter and λ(c) the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, α∼U(-1), but with different prefactors depending on the value of Bo(D). For small Bo(D) (large capillary effects), the wake angle approximately follows the law α≃c(g,min)/U, where c(g,min) is the minimum group velocity of capillary-gravity waves. For larger Bo(D) (weak capillary effects), we recover a law α∼√[gD]/U similar to that found for ship wakes at large velocity [Rabaud and Moisy, Phys. Rev. Lett. 110, 214503 (2013)]. Using the general property of dispersive waves that the characteristic wavelength of the wave packet emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. We show that the new capillary law α≃c(g,min)/U originates from the presence of a capillary cusp angle (distinct from the usual gravity cusp angle), along which the energy radiated by the disturbance accumulates for Bond numbers of order of unity. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in qualitative agreement with experimental measurements.