斜坡床面上潜水员诱导黏性粉砂起动降阶动力学模型
A Reduced-Order Dynamical Model for the Ignition of Diver-Induced Cohesive Silt-Out on Sloping Beds
AI总结：
该研究建立了一个降阶动力学模型，通过三个无量纲组和鞍点稳定流形，确定了潜水员诱导粉砂起动在斜坡上的点火阈值，并发现床面坡度是控制参数。
AI中文摘要：
靠近黏性海床的下向鳍推力会使沉积物扬起。该沉积物云是沉降下来，还是组织成自维持的下坡流，决定了潜水员是短暂失去能见度还是遭遇灾难性后果。我们在弱夹带极限下，将流体质量、沉积物质量和动量的层平均平衡简化为固定厚度的时变板块。这产生了一个无量纲近底速度和悬移质载荷的自洽平面向量场，由三个无量纲组控制：沉降阻力、侵蚀强度和近底浓度。该场在原点处存在一个静止平衡点，并且当底床坡度超过临界值（以封闭形式给出，为近底浓度乘以沉降阻力数再除以侵蚀强度数之比）时，存在一个内部鞍点平衡。鞍点的稳定流形将状态空间划分为衰减域和无界增长域，确立了自限制扰动与点火扰动之间的精确阈值。在平坦床面上，对于所有可容许的侵蚀定律，原点全局吸引。对于代表性粉砂，点火阈值接近17度床面角。封闭形式结构经数值验证达到机器精度。闭合研究表明，临界坡度在存在性上是稳健的，但在数值上依赖于闭合形式，线性侵蚀定律被确定为保守选择。因此，该模型将床面坡度确定为点火的控制参数。
英文摘要：
A downward fin thrust near a cohesive seabed lofts sediment. Whether this cloud settles or organizes into a self-sustaining down-slope current determines if a diver loses visibility briefly or catastrophically. We reduce the layer-averaged balances of fluid mass, sediment mass, and momentum to a temporal slab of fixed thickness in the weakly entraining limit. This yields an autonomous planar vector field in dimensionless near-bed speed and suspended load, governed by three dimensionless groups: drag against settling, erosion strength, and near-bed concentration. The field possesses a quiescent equilibrium at the origin and, above a critical bed slope obtained in closed form as the ratio of near-bed concentration times drag-settling number to erosion-strength number, an interior saddle equilibrium. The saddle's stable manifold partitions the state space into basins of decay and unbounded growth, establishing the exact threshold between self-limiting and igniting disturbances. On a flat bed, the origin attracts globally for all admissible erosion laws. For representative silt, the ignition threshold is near a 17-degree bed angle. The closed-form structure is confirmed numerically to machine precision. A closure study demonstrates the critical slope is robust in existence but closure-dependent in value, identifying the linear erosion law as the conservative choice. The model thus isolates bed slope as the controlling parameter for ignition.
