Song of the dunes as a self-synchronized instrument

Granular temperature measured experimentally in a shear flow by acoustic energy

Granular temperature may control high-speed granular flows, yet it is difficult to measure in laboratory experiments. Here we utilize acoustic energy to measure granular temperature in dense shear flows. We show that acoustic energy captures the anticipated behavior of granular temperature as a function of grain size in quartz sand shear flows. We also find that granular temperature (through its proxy acoustic energy) is nearly linearly proportional to inertial number, and dilation is proportional to acoustic energy raised to the power 0.6±0.2. This demonstrates the existence of a relationship between granular temperature and dilation. It is also consistent with previous results on dilation due to externally imposed vibration, thus showing that internally and externally induced vibrations have identical results on granular shear flows.

Friction and the oscillatory motion of granular flows

This contribution reports on numerical simulations of two-dimensional granular flows on erodible beds. The broad aim is to investigate whether simple flows of model granular matter exhibit spontaneous oscillatory motion in generic flow conditions, and in this case, whether the frictional properties of the contacts between grains may affect the existence or the characteristics of this oscillatory motion. The analysis of different series of simulations shows that the flow develops an oscillatory motion with a well-defined frequency which increases like the inverse of the velocity's square root. We show that the oscillation is essentially a surface phenomenon. The amplitude of the oscillation is higher for lower volume fractions and can thus be related to the flow velocity and grains' friction properties. The study of the influence of the periodic geometry of the simulation cell shows no significant effect. These results are discussed in relation to sonic sands.

Probing the shear-band formation in granular media with sound waves

We investigate the mechanical responses of dense granular materials, using a direct shear box combined with simultaneous acoustic measurements. Measured shear wave speeds evidence the structural change of the material under shear, from the jammed state to the flowing state. There is a clear acoustic signature when the shear band is formed. Subjected to cyclic shear, both shear stress and wave speed show the strong hysteretic dependence on the shear strain, likely associated with the geometry change in the packing structure. Moreover, the correlation function of configuration-specific multiply scattered waves reveals an intermittent behavior before the failure of material.

Sonic sands

Many desert sand dunes emit a loud sound with a characteristic tremolo around a well-defined frequency whenever sand is avalanching on their slip face. This phenomenon, called the 'song of dunes', has been successfully reproduced in the lab, on a smaller scale. In all cases, the spontaneous acoustic emission in air is due to a vibration of the sand, itself excited by a granular shear flow. This review presents a complete characterization of the phenomenon-frequency, amplitude, source shape, vibration modes, instability threshold-based on recent studies. The most prominent characteristics of acoustic propagation in weakly compressed granular media are then presented. Finally, this review describes the different mechanisms proposed to explain booming avalanches. Measurements performed to test these theories against data allow one to contrast explanations that must be rejected-sound resonating in a surface layer of the dune, for instance-with those that still need to be confirmed to reach a scientific consensus-amplification of guided elastic waves by friction, in particular.

Relevance of numerical simulations to booming sand

We have performed a simulation study of three-dimensional cohesionless granular flows down an inclined chute. We find that the oscillations observed in [L. E. Silbert, Phys. Rev. Lett. 94, 098002 (2005)] near the angle of repose are harmonic vibrations of the lowest normal mode. Their frequencies depend on the contact stiffness as well as on the depth of the flow. Could these oscillations account for the phenomena of "booming sand"? We estimate an effective contact stiffness from the Hertz law, but this leads to frequencies that are several times higher than observed. However, the Hertz law also predicts interpenetrations of a few nanometers, indicating that the oscillations frequencies are governed by the surface stiffness, which can be much lower than the bulk one. This is in agreement with previous studies ascribing the ability to sing to the presence of a soft coating on the grain surface.

Laboratory singing sand avalanches

Some desert sand dunes have the peculiar ability to emit a loud sound up to 110 dB, with a well-defined frequency: this phenomenon, known since early travelers (Darwin, Marco Polo, etc.), has been called the song of dunes. But only in late 19th century scientific observations were made, showing three important characteristics of singing dunes: first, not all dunes sing, but all the singing dunes are composed of dry and well-sorted sand; second, this sound occurs spontaneously during avalanches on a slip face; third this is not the only way to produce sound with this sand. More recent field observations have shown that during avalanches, the sound frequency does not depend on the dune size or shape, but on the grain diameter only, and scales as the square root of g/d--with g the gravity and d the diameter of the grains--explaining why all the singing dunes in the same vicinity sing at the same frequency. We have been able to reproduce these singing avalanches in laboratory on a hard plate, which made possible to study them more accurately than on the field. Signals of accelerometers at the flowing surface of the avalanche are compared to signals of microphones placed above, and it evidences a very strong vibration of the flowing layer at the same frequency as on the field, responsible for the emission of sound. Moreover, other characteristics of the booming dunes are reproduced and analyzed, such as a threshold under which no sound is produced, or beats in the sound that appears when the flow is too large. Finally, the size of the coherence zones emitting sound has been measured and discussed.

Booming dune instability

Sand avalanches flowing down the leeward face of some desert dunes spontaneously produce a loud sound with a characteristic vibrato around a well-defined frequency, a phenomenon called the "song of dunes." Here, we show through theory that a homogenous granular surface flow is linearly unstable towards growing elastic waves when a localized shear band forms at the interface between the avalanche and the static part of the dune. We unravel the nature of the acoustic amplifying mechanism at the origin of this booming instability. The dispersion relation and the shape of the most unstable modes are computed and compared to field measurements.

Mechanisms for acoustic absorption in dry and weakly wet granular media

The dissipation of an elastic wave in dry and wet glass bead packings is measured using multiple sound scattering. The interplay of a linear viscoelastic loss and a nonlinear frictional one is observed in dry media. The Mindlin model provides a qualitative description of the experiment, but fails to quantitatively account for the data due to grain roughness. In weakly wet media, we find that the dissipation is dominated by a linear viscous loss due to the liquid films trapped at the grain surface asperities. Adding more liquid enables us to form the capillary menisci but does not increase the energy loss.

Avalanche dynamics on a rough inclined plane

The avalanche behavior of gravitationally forced granular layers on a rough inclined plane is investigated experimentally for different materials and for a variety of grain shapes ranging from spherical beads to highly anisotropic particles with dendritic shape. We measure the front velocity, area, and height of many avalanches and correlate the motion with the area and height. We also measure the avalanche profiles for several example cases. As the shape irregularity of the grains is increased, there is a dramatic qualitative change in avalanche properties. For rough nonspherical grains, avalanches are faster, bigger, and overturning in the sense that individual particles have down-slope speeds u p that exceed the front speed uf as compared with avalanches of spherical glass beads that are quantitatively slower and smaller and where particles always travel slower than the front speed. There is a linear increase of three quantities: (i) dimensionless avalanche height, (ii) ratio of particle to front speed, and (iii) the growth rate of avalanche speed with increasing avalanche size with increasing tan theta r where theta r is the bulk angle of repose, or with increasing beta P, the slope of the depth averaged flow rule, where both theta r and beta P reflect the grain shape irregularity. These relations provide a tool for predicting important dynamical properties of avalanches as a function of grain shape irregularity. A relatively simple depth-averaged theoretical description captures some important elements of the avalanche motion, notably the existence of two regimes of this motion.

Flow rule of dense granular flows down a rough incline

We present experimental findings on the flow rule for granular flows on a rough inclined plane using various materials, including sand and glass beads of various sizes and four types of copper particles with different shapes. We characterize the materials by measuring hs (the thickness at which the flow subsides) as a function of the plane inclination theta on various surfaces. Measuring the surface velocity u of the flow as a function of flow thickness h, we find that for sand and glass beads the Pouliquen flow rule u/sqrt[gh] approximately betahhs provides reasonable but not perfect collapse of the u(h) curves measured for various theta and mean particle diameter d. Improved collapse is obtained for sand and glass beads by using a recently proposed scaling of the form u/sqrt[gh]=betahtan2theta/hstan2theta1 where theta1 is the angle at which the hs(theta) curves diverge. Measuring the slope beta for ten different sizes of sand and glass beads, we find a systematic, strong increase of beta with the divergence angle theta1 of hs. Copper materials with different shapes are not well described by either flow rule with u approximately h3/2.

Surface elastic waves in granular media under gravity and their relation to booming avalanches

Due to the nonlinearity of Hertzian contacts, the speed of sound c in granular matter is expected to increase with pressure as P(1/6). A static layer of grains under gravity is thus stratified so that the bulk waves are refracted toward the surface. The reflection at the surface being total, there is a discrete number of modes (both in the sagittal plane and transverse to it) localized close to the free surface. The shape of these modes and the corresponding dispersion relation are investigated in the framework of an elastic description taking into account the main features of granular matter: Nonlinearity between stress and strain and the existence of a yield transition. We show in this context that the surface modes localized at the free surface exhibit a waveguide effect related to the nonlinear Hertz contact. Recent results about the song of dunes are reinterpreted in light of the theoretical results. The predicted propagation speed is compared with measurements performed in the field. Taking into account the finite depth effects, we show that the booming instability threshold can be explained quantitatively by a waveguide cutoff frequency below which no sound can propagate. Therefore, we propose another look at a recent controversy, confirming that the song of dunes can well originate from a coupling between avalanching grains and surface elastic waves once the specificity of surface waves (we baptized Rayleigh-Hertz) is correctly taken into account.