鸣沙沙粒振动频率自锁机制
The Mode Locking of the Booming Sand Dunes

摘要 研究在30°安息角的沙坡面上, 单一粒径球形沙粒的运动状态。假设沙粒无滑动且碰撞时角动量守恒, 则扰动沙粒经过不超过5 次的滚动、抛射、再滚动后，即进入与初条件无关的周期性运动, 其频率为0.39 g/D , 与鸣沙流的梯度相近, 临界抛射角稳定在 51.2°, 抛射过程沙粒自旋角速度为 16 r/min。自保持的周期性决定了沙粒的整体协同运动, 是鸣沙发声及频率自锁的根本原因。
Abstract A two layer model is developed to investigate the movement of a single round particle. The reference layer is set as a slope with the repose angle 30°, and is covered regularly with round particles with the same diameter. The free layer in which the same diameter can move freely is just on the reference layer. A periodic rolleject- collide movement is found, and the frequency is 0.39 g/D , which is independent of the initial velocity and close to the velocity gradient. The constant projection angle is 51.2° and the spin angular velocity is 16 r/min. This self-hold of frequency determines the sands in the free layer to move forwards integrally, and may be the basic acoustic mechanism of the booming sands.