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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 ∼ 1), for decreasing St, the amplitude decreases and the time duration increases, exploring an inertial regime and a viscous regime. These regimes are described by the analysis of the elementary motion of one grain. Granular matter has received much attention from physicists over the past few years [1]. Beyond the fundamental interest in the physics of granular systems which can present some features of either solids, liquids or even gases, the understanding of granular materials is essential in many industrial activities such as pharmacology, chemical engineering, food, agriculture, and so on. Many studies concern the avalanches that may arise on the slope of a granular pile in air. Such granular avalanches occur in various places in Nature, from small scale, as for the building of any sand pile, to large scale, as the event observed after the Mont St-Helen eruption in 1980. Two angles can be defined when building a pile: the maximum angle of stability θ m at which an avalanche starts and the angle of repose θ r at which the avalanche stops. Between these two angles is a region of bistability where the grains can either be flowing ("liquid state") or at rest ("solid state"). Many experiments performed with dry grains in a rotating cylinder [2,3,4,5,6] showed clearly the existence of these two angles.To date, no detailed study has focused on the influence of the interstitial fluid for a totally immersed grain assembly. This influence is certainly important in granular avalanche processes, as evidenced by the marked differences observed by geologists between subaqueous and eolian cross strata [7]. As a matter of fact, the propagation of subaqueous dunes differs in general from the propagation of eolian dunes even if the slope angles are quite similar: When the transport rate of sand particles is large enough, the flow is continuous in the lee side of the structure in the immersed case, but occurs by successive avalanches in the dry case [7]. This observation prompted geologists to accumulate data on avalanches of sand or beads in rotating drums filled with air or water [8] or even with glycerol mixtures [9], that seemed to show that the amplitude of avalanches decreases and the time duration increases with the fluid viscosity. We have performed an extensive series of experiments to investigate the influence of the interstitial fluid on the packing stability and the avalanche dynamics. The analysis of our results obtained with a rotating drum set-up indicate the existence of three regimes: (i) a free-fall regime for which there is no fluid influence and that corresponds to the classical dry regime, and two regimes where the interstitial fluid governs the a...

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 ⍀ −1 ͑⍀ is the rotation rate͒, until the friction from the Ekman layers becomes dominant. The energy spectrum perpendicular to the rotation axis becomes steeper as the instantaneous Rossby number Ro = Ј /2⍀ decreases below the value 2 ± 0.5 ͑Ј is the root-mean square of the vertical vorticity͒. The spectral exponent increases in time from its classical Kolmogorov value 5 / 3 up to values larger than 2. Below the threshold Ro Ͻ 2, the velocity derivative skewness decreases as ͉S͉ ϰ Ro , reflecting the inhibition of the energy transfers by the background rotation, with a net inverse energy cascade that develops at large scales.

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 o 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 F r = U/ √ gL 0.5, where L is the hull ship length.

We study experimentally the parallel flow in a Hele-Shaw cell of two immiscible fluids, a gas and a viscous liquid, driven by a given pressure gradient. We observe that the interface is destabilized above a critical value of the gas flow and that waves grow and propagate along the cell. The experimental threshold corresponds to a velocity difference of the two fluids in good agreement with the inviscid Kelvin-Helmholtz instability, while the wave velocity corresponds to a pure viscous theory deriving from Darcy's law. We report our experimental results and analyze this instability by the study of a new equation where the viscous effects are added to the Euler equation through a unique drag term. The predictions made from the linear stability analysis of this equation agree with the experimental measurements.

The Saffman–Taylor fingers are studied in cells that have the form of sectors of a disk. The less viscous fluid can be injected at the apex (divergent flow) or at the periphery (convergent flow). As in the linear geometry, at large velocities, a unique finger tends to occupy a well determined fraction λ of the cell angular width. This fraction is a function of the angle of the cell, being larger than 0.5 in the divergent case and smaller in the convergent case. In both cases these fractions tend linearly toward λ=0.5 when the angle of the cell tends to zero. In support of recent theories, these results show how the selection is changed when the geometry induces an increase or a decrease of the curvature of the profiles. The formation of fingers in the circular geometry is revisited. In a divergent flow, the circular front appears to break into independent parts so that each finger grows as if it were contained in a sector shaped cell. The rate of occupancy of the cell by one of the fluids as a function of the distance to the center is then discussed. Finally, the existence of the mathematical counterpart to the well-known Saffman–Taylor finger solutions in a nonparallel cell is discussed in the Appendix.

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