论文标题
分散滑坡
Dispersive landslide
论文作者
论文摘要
考虑到非静态质量流量模型（Pudasaini，2022），我们在这里得出了一种新型的滑坡分散波方程。新的滑坡分散浪潮将经典的分散水波恢复为特殊情况。我们表明，滑坡的频率分散关系与水波的经典频率分散固有不同。随着波浪数的函数，带有色散的波频率非线性增加。对于色散滑坡，没有色散的波频率似乎高估了较高波浪数的分散波频率。由于分散术语是从非静态贡献的滑坡贡献中出现的，因此相速度成为波数的函数。这引起了组速度，该速度与相位速度显着不同，表征了分散质量流。分散相速度和组速度随波数非线性降低。然而，组速度大大低于相速度。我们通过分析得出一个分散数，作为相位速度与组速度之间的比率，该比率衡量了组速度偏离相速度的偏差，它在它们之间提供了动态缩放，并总结了质量流中分散体的总体效果。滑坡的分散数随波浪数迅速增加，这与水波的分散相反。通过定义有效的分散性侧向应力，我们证明了在滑坡中存在抗恢复力。我们揭示了这样一个事实，即由于反恢复力量，滑坡比钢琴弦更分散。因此，滑坡中的波散与钢琴弦中的波色散根本不同。我们的模型构成了分散质量流中波浪现象的基础。
Considering the non-hydrostatic mass flow model (Pudasaini, 2022), here, we derive a novel dispersive wave equation for landslide. The new dispersive wave for landslide recovers the classical dispersive water waves as a special case. We show that the frequency dispersion relation for landslide is inherently different than the classical frequency dispersion for water waves. The wave frequency with dispersion increases non-linearly as a function of the wave number. For dispersive landslide, the wave frequency without dispersion appears to heavily overestimate the dispersive wave frequency for higher wave number. Due to the dispersion term emerging from the non-hydrostatic contribution for landslide, the phase velocity becomes a function of the wave number. This gives rise to the group velocity that is significantly different from the phase velocity, characterizing the dispersive mass flow. The dispersive phase velocity and group velocity decrease non-linearly with the wave number. Yet, the group velocity is substantially lower than the phase velocity. We analytically derive a dispersion number as the ratio between the phase velocity and the group velocity, which measures the deviation of the group velocity from the phase velocity, provides a dynamic scaling between them and summarizes the overall effect of dispersion in the mass flow. The dispersion number for landslide increases rapidly with the wave number, which is in contrast to the dispersion in water waves. With the definition of the effective dispersive lateral stress, we prove the existence of an anti-restoring force in landslide. We reveal the fact that due to the anti-restoring force, landslides are more dispersive than the piano strings. So, the wave dispersion in landslide is fundamentally different than the wave dispersion in the piano string. Our model constitutes a foundation for the wave phenomenon in dispersive mass flows.
