幂律流底泥的质量输移和流场

Mass transport and flow field of power law muddy bed under surface waves

基于欧拉坐标系,在波浪与底泥相互作用的两层系统中,对表面波作用下底泥的质量输移进行理论研究.上层为水;下层为底泥,用幂律流模型描述;波动由施加在在自由水表面上的周期性压力荷载驱动.基于浅水波和小变形假设,采用摄动分析将运动方程和边界条件展开到二阶问题,并采用数值迭代法计算求解非线性微分方程.分析幂律流流动指数和压力荷载的变化对流场分布、质量输移速度以及自由水面和泥-水界面位置变化的影响.结果发现,随着幂律流流动指数的减小,由于受到界面剪切作用,泥-水界面附近流场中出现环流结构和流动间歇性停止现象,同时质量输移速度迅速减小.为验证理论分析的正确性,将质量输移速度计算结果与水槽试验结果进行对比,结果发现两者吻合较好.

A theoretical study on the mass transport and the flow field in muddy bed due to surface waves was performed based on Eulerian coordinates system. In the two-layer system, the fluid in the upper layer was clear water, and mud in the lower layer was modelled as a power-law medium; the wave motion was driven by the periodic pressure on the water surface. According to the assumptions of shallowness and small deformations, a perturbation analysis was carried out to the second order; the numerical iteration method was employed to solve the non-linear governing equation at the leading order. With change of the power-law flow index and the pressure load, the flow field and the mass transport velocity were examined; the free water surface and interfacial set-ups were also found as a part of the solutions. It turns out that, as the flow index decreases, the velocity value in the upper layer diminishes and the rotation of the cells in the upper layer eventually reverses; the circulation structure appears near the interface, because of the in-terfacial shearing. The mass transport velocity also decreases rapidly with the decreasing of flow index. The verification is given by comparing the calculated results with the experimental results in the literature, which shows a good agreement.