发表机构
Department of Mathematics and Manchester Centre for Nonlinear Dynamics, University of Manchester（曼彻斯特大学数学系与曼彻斯特非线性动力学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过截面平均稳定性分析及实验，发现凸形通道约束可抑制重力流滚动波不稳定性，并可用无量纲参数预测，对自然河道观测有启示。
AI 中文摘要
在某些条件下，重力流会在其自由表面自发发展出大幅度的流向起伏（“滚动波”）。本文研究了通道几何形状对该不稳定性的影响。通过独立于流动材料流变学的截面平均稳定性分析，发现相对于无约束流动，凸形开放通道具有稳定作用。这与在梯形通道中进行的横向浅水流和干颗粒材料流的实验观察结果一致。对于此类流动，几何形状的影响可由单个无量纲参数表征，该参数预测随着通道宽度变窄，流动趋于稳定。在分析中纳入横向速度剖面进一步使预测趋于稳定，并可使三角通道中的稳态流动无条件稳定——这一发现得到了我们实验的证实。因此，横向倾斜梯形通道也可以通过将润湿区域调整为近似三角形来稳定流动。通过将瑞士伊尔格拉本（Illgraben）现有的滚动波模型进行改造以纳入通道几何形状，考虑了对自然河道观测结果的影响。所得模拟对真实横截面产生了合适的波浪，但适度的通道变窄会使波浪趋于稳定。随后构建了互补的非线性波解，并用于表明通道约束也会减小观测到的波浪振幅。最后，讨论了分析的例外情况，包括静态材料可能屏蔽几何效应的影响。我们通过观察在三角槽中穿过静止沉积物的未衰减颗粒雪崩来证明这一点。
英文摘要
Under certain conditions, gravity currents spontaneously develop large-amplitude streamwise undulations on their free surfaces ('roll waves'). The effect of channel geometry on this instability is investigated herein. Via a section-averaged stability analysis conducted independently of the rheology of the flowing material, convex open channels are found to be stabilising, relative to unconfined flows. This is shown to agree with experimental observations of laterally shallow currents of water and dry granular material in trapezoidal channels. For such flows, the influence of the geometry can be characterised by a single dimensionless parameter, which predicts stabilisation as the channel width narrows. Including the cross-stream velocity profile in the analysis further stabilises predictions and can render steady flows in triangular channels unconditionally stable - a finding borne out by our experiments. Consequently, laterally tilting a trapezoidal channel can also stabilise flows by adjusting the wetted region towards a triangular one. Implications for observations in natural channels are considered by adapting an existing model of roll waves in the Illgraben, Switzerland, to incorporate channel geometry. The resulting simulations produce suitable waves for a realistic cross-section, but are stabilised by a modest narrowing of the channel. Complementary nonlinear wave solutions are then constructed and used to show that channel confinement also diminishes amplitudes of observed waves. Finally, exceptions to the analysis are discussed, including the possibility for static material to shield waves from the effects of geometry. We demonstrate this using observations of undamped granular avalanches travelling through an arrested deposit in a triangular chute.
Comments35 pages, 14 figures, 3 ancillary movies. Submitted to the Journal of Fluid Mechanics
