Physique et Mécanique des Milieux Hétérogènes, UMR 7636 CNRS-ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France.
Phys Rev Lett. 2009 Dec 4;103(23):238001. doi: 10.1103/PhysRevLett.103.238001. Epub 2009 Dec 1.
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.
沙丘下风面流动的沙流会自发产生一种响亮的声音，伴有特征性的震音，频率明确，这种现象被称为“沙丘之歌”。在这里，我们通过理论表明，当滑坡与沙丘静止部分之间的界面形成局部剪切带时，均匀的颗粒表面流对于弹性波的增长是线性不稳定的。我们揭示了这种隆隆不稳定性的声学放大机制的本质。计算并比较了色散关系和最不稳定模式的形状与现场测量结果。
