Sharp Transition in the Lift Force of a Fluid Flowing Past Nonsymmetrical Obstacles: Evidence for a Lift Crisis in the Drag Crisis Regime.

Bluff bodies moving in a fluid experience a drag force which usually increases with velocity. However in a particular velocity range a drag crisis is observed, i.e., a sharp and strong decrease of the drag force. This counterintuitive result is well characterized for a sphere or a cylinder. Here we show that, for an object breaking the up-down symmetry, a lift crisis is observed simultaneously to the drag crisis. The term lift crisis refers to the fact that at constant incidence the time-averaged transverse force, which remains small or even negative at low velocity, transitions abruptly to large positive values above a critical flow velocity. This transition is characterized from direct force measurements as well as from change in the velocity field around the obstacle.

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.

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 ship's 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.

Transition by intermittency in granular matter: from discontinuous avalanches to continuous flow.

We investigate, in the rotating drum configuration, the transition from the regime of discontinuous avalanches observed at low angular velocity to the regime of continuous flow observed at higher velocity. Instead of the hysteretic transition reported previously by Rajchenbach [Phys. Rev. Lett. 65, 2221 (1990)], with an apparent bistability of the two flow regimes in a range of drum velocities, we observe intermittency with spontaneous erratic switches from one regime to the other. Both scenarios of transition are recovered by a model dynamic equation for the avalanche flow with two sources of stochasticity: a Langevin noise during the avalanche flow and a distributed maximal stability angle at which avalanches start.

Dynamics of dry granular avalanches.

A fine analysis of the statistics of dry granular avalanches in a rotating drum setup reveals that, beyond the fluctuations, the angle at which an avalanche ends is correlated experimentally to the angle at which the avalanche starts. This correlation resulting from inertia defines an intermediate "neutral" angle that characterizes the corresponding granular pile. In addition, an intensive study of the dynamics of the avalanche shows that the time duration of the avalanche is correlated to its amplitude, being smaller for higher amplitude. The time relaxation of the pile slope during any avalanche, governed by the deviation of the starting angle from the neutral angle, follows a master curve. A simple model recovers most of the results and contributes to a better understanding of the physics of the avalanche flow.

Instantaneous velocity profiles during granular avalanches.

We perform experimental measurements of the instantaneous velocity profile of the flowing layer during granular avalanches. In the pile depth, the velocity profile follows a pure exponential decrease in contrast with steady flows that are known to exhibit a well developed upper linear part. The velocity profile in the pile width is a plug flow with two exponential boundary layers at the walls. Even though no steady state is observed during the avalanche, these velocity profiles are self-similar and build up almost instantaneously, with time independent characteristic lengths.

Granular avalanches in fluids.

Three regimes of granular avalanches in fluids are put in light depending on the Stokes number St which prescribes the relative importance of grain inertia and fluid viscous effects and on the grain/fluid density ratio r. In gas (r>>1 and St>1, e.g., the dry case), the amplitude and time duration of avalanches do not depend on any fluid effect. In liquids (r approximately 1), for decreasing St, the amplitude decreases and the time duration increases, exploring an inertial regime and a viscous regime. These three regimes are described by the analysis of the elementary motion of one grain.