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

Abstract

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.

Orientation towards prey in antlions: efficient use of wave propagation in sand

“…Wave propagation within granular materials has been studied only recently (Liu and Nagel, 1992;Somfai et al, 2005) and even more recently in sand (Bonneau et al, 2007). In a granular medium, waves travel along specific paths determined by the geometrical arrangement of sand grains, which itself defines a contact network between grains.…”

Multiple Scattering of Elastic Waves in Granular Media: Theory and Experiments

“…It is necessary a systematic study of the transport properties of elastic waves between the different regimes of external load: strong compression ↔ weak compression ↔ zero compression. The last one is related to the behavior of waves at the free surface of the granular packing (Bonneau et al (2007;2008) ;Gusev et al (2006)). The propagation of sound at the surface of sand is related to the localization of preys by scorpions (Brownell (1977)) and the spontaneous emission of sound by sand avalanches (the so-called song of dunes) (Bonneau et al (2007)).…”

“…The last one is related to the behavior of waves at the free surface of the granular packing (Bonneau et al (2007;2008) ;Gusev et al (2006)). The propagation of sound at the surface of sand is related to the localization of preys by scorpions (Brownell (1977)) and the spontaneous emission of sound by sand avalanches (the so-called song of dunes) (Bonneau et al (2007)). We believe that the experiments presented in this chapter point out to the considerable interest in acoustic probing as a tool for studying of the mechanical properties of confined granular media.…”

“…The authors interpreted this as being due to sound propagating within the granular medium predominantly along strong force chains. In recent years, our understanding of wave propagation in granular materials has advanced both experimentally and theoretically, covering topics such as surface elastic waves, booming avalanches (Bonneau et al (2007;2008)), earthquake triggering (Johnson & Jia (2005)), and coda-like scattered waves (Jia et al (1999); Jia (2004); Jia et al (2009)). The understanding of wave motion in granular media took a major step forward with the experimental observation of the coexistence of a coherent ballistic pulse travelling through an "effective contact medium" and a multiply scattered signal (Jia et al (1999)).…”

Singing sands, booming dune sands, and the stick–slip effect

“…Subsequent reports by Bonneau et al [5,6] go to great lengths to elucidate the properties of waves propagating along a dune surface where the elastic moduli increase with sand depth.…”