长距离泥石流中孤立波模式的可接受性
Admissibility of Solitary Wave Modes in Long-Runout Debris Flows
AI总结：
研究通过KdV方程分析长距离泥石流中缓坡段的孤立波模式，探讨其可接受性及非线性诊断方法。
摘要：
泥石流常常表现出相干波结构——在陡坡上表现为类似激波的卷波，在缓坡上则表现为弱而更正弦状的分散脉冲。粗颗粒的头部增加底部阻力，而细颗粒的尾部降低它；在缓坡段，小振幅脉冲可以局部地在低阻力段传输动量。我们关注这一缓坡、长波、低振幅的 regime，其中底流弗劳德数为数量级一。在这一极限下，我们从平均深度平衡中得到Korteweg-de Vries（KdV）的简化，使用长波小k regime中的曲率型内部法向应力闭合，考虑摩擦（库仑）和粘性塑性底部选项。多重尺度分析得到有效的非线性和色散系数。我们还引入了一个实用的非线性诊断，可通过观测的波峰速度和流量厚度计算得出。当实验室框架的波峰速度可用时，我们通过KdV速度振幅关系估计一个有效的二次系数，并报告其与浅水参考的比率。当只有平均深度第一波速度和厚度可用时，我们使用相同的方法构建一个基于速度的代理，并注意其在零附近存在偏差。弗劳德-坡度图将已发表的案例分为陡坡卷波域和KdV脉冲可接受的缓坡走廊。全深度平均模型的数值解产生cnoidal和孤立波，这些在该走廊内与简化KdV预测一致。我们将色散脉冲视为特定于该区域的补充，为缓坡上的移动提供条件依赖性的贡献，而不是对长距离运行的普遍解释。
英文摘要：
Debris flows often exhibit coherent wave structures-shock-like roll waves on steeper slopes and weaker, more sinusoidal dispersive pulses on gentler slopes. Coarse-rich heads raise basal resistance, whereas fines-rich tails lower it; in gentle reaches, small-amplitude pulses can locally transport momentum across low-resistance segments. We focus on this gentle-slope, long-wave, low-amplitude regime, where the base-flow Froude number is order unity. In this limit, we obtain a Korteweg-de Vries (KdV) reduction from depth-averaged balances with frictional (Coulomb) and viscous-plastic basal options, using a curvature-type internal normal-stress closure in the long-wave small-k regime. Multiple-scale analysis yields effective nonlinear and dispersive coefficients. We also introduce a practical nonlinearity diagnostic that can be computed from observed crest speeds and flow thicknesses. When laboratory-frame crest celerity is available, we estimate an effective quadratic coefficient from the KdV speed-amplitude relation and report its ratio to the shallow-water reference. When only a depth-averaged first-surge speed and thickness are available, we use the same construction to form a velocity-based proxy and note its bias near zero. A Froude-slope diagram organizes published cases into a steep-slope roll-wave domain and a gentle-slope corridor where KdV pulses are admissible. Numerical solutions of the full depth-averaged model produce cnoidal and solitary waves that agree with the reduced KdV predictions within this corridor. We regard dispersive pulses as a regime-specific complement to roll-wave dynamics, offering a condition-dependent contribution to mobility on gentle reaches rather than a universal explanation for long runout.
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