离散型滑坡
Dispersive landslide
摘要：
考虑非静力质量流模型（Pudasaini，2022），本文推导了一种新的滑坡色散波动方程式方程。新的滑坡频散波恢复了经典频散水波的特殊情况。我们表明，频率频散关系的滑坡是本质上不同于经典的频率色散水波。具有色散的波频作为波数的函数非线性地增加。对于分散型滑坡，无分散的波频似乎严重高估了较高波数的分散波频。由于滑坡的非流体静力学贡献中出现了频散项，因此相速度成为波数的函数。这导致了显著不同于相速度的群速度，表征了分散的质量流。色散相速度和群速度随波数的增加呈非线性减小。然而，群速度基本上低于相速度。我们解析地推导出色散数作为相速度和群速度之间的比率，其测量群速度与相速度的偏差，提供了它们之间的动态缩放，并总结了质量流中色散的整体效果。滑坡的频散数随波数的增加而迅速增加，这与水波的频散相反。通过定义有效弥散側向应力，证明了滑坡存在反回复力。我们揭示了一个事实，由于反回复力，滑坡是更分散的比钢琴弦。因此，滑坡中的波频散与钢琴弦中的波频散有着根本的不同。我们的模型构成了一个基础的波现象在分散的质量流。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
