Linear and nonlinear wave propagation in booming sand dunes

Abstract

The current field study examines linear and non-linear acoustic waves found in large desert sand dunes using field measurements of wave speed, frequency content, dispersion, and polarization. At the dune fields visited, an avalanching of sand can trigger a loud booming or rumbling sound with narrow peak frequencies centered between 70 and 105 Hz with higher harmonics. Prior to the onset of the nearly monotone booming, the emission consists of short bursts or burps of sound of smaller amplitude and over a significantly broader range of frequencies. These burps created at dune sites have similar frequency content to sounds generated by small-scale shearing in laboratory-scale experiments. By investigating the wave characteristics of both burping and booming emissions, this manuscript demonstrates that booming and burping correspond with the transmission of different waves within the dune. The burping sounds correspond to a surface Rayleigh wave with nonlinear and dispersive properties. The booming emission results from a linear, non-dispersive P-wave, which supports an earlier analysis where booming is modeled as the trapping of the body waves in the dune’s surficial layer. Besides characterizing the booming and burping emissions, this manuscript illustrates the effect of scale in the wave propagation of granular materials, when non-linear, dispersive waves across small scales transition to linear, non-dispersive waves across larger scales.