Surface elastic waves in granular media under gravity and their relation to booming avalanches.
Surface elastic waves in granular media under gravity and their relation to booming avalanches.
复制标题
重力作用下颗粒介质中的表面弹性波及其与爆发雪崩的关系。
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Eric Clément
中科院分区：
文献类型：
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作者：
L. Bonneau;Bruno Andreotti;Eric Clément
由于赫兹接触的非线性，颗粒物质中的声速c预计随着压力P（1/6）而增加。在重力作用下，静止的颗粒层就这样分层，从而使体波向表面折射。表面处的反射是全反射，存在靠近自由表面局部化的离散数量的模式（在矢状平面中和横向于矢状平面）。这些模式的形状和相应的色散关系的弹性描述的框架中进行了研究，考虑到颗粒物质的主要特点：应力和应变之间的非线性和屈服过渡的存在。在这种情况下，我们表明，在自由表面局部化的表面模式表现出与非线性赫兹接触的波导效应。根据理论结果，对沙丘之歌的最新研究结果进行了重新解释。预测的传播速度进行比较，在现场进行的测量。考虑到有限深度的影响，我们表明，蓬勃发展的不稳定性阈值可以定量地解释波导截止频率，低于没有声音可以传播。因此，我们提出另一个看看最近的争议，确认歌曲的沙丘可以很好地起源于雪崩颗粒和表面弹性波之间的耦合，一旦表面波的特异性（我们受洗瑞利赫兹）被正确地考虑。
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.