柔性浮板对缓坡水流动力特性的影响
Effect of floating flexible plate on the dynamics of flow over a mild-slope
摘要：
本文研究了重力驱动下沿斜面流动的流体动力学不稳定性，其中在流动的顶面上放置了一个浮动的弹性板。线性不稳定性的系统相对于无穷小的干扰被捕获使用正常模式分析。利用长波近似和小膜厚比，得到了不稳定的临界条件。进一步，利用弱非线性稳定性分析方法分析了非线性发展方程的分支。推导了扰动流的Orr-Sommerfeld方程组，并采用谱配置法进行了数值求解。描绘了一系列无量纲流动参数的边际稳定性曲线和不稳定波的时间增长的行为。此外，还计算和分析了各种结构和流动构型下的表面压力和剪应力。研究表明，关键的结构参数，如刚度和单位长度的质量起着至关重要的作用，抑制和促进不稳定的表面波的流动。数值结果表明，弹性浮板有助于稳定表面流场，并对高振幅波起到阻尼作用。
英文摘要：
Hydrodynamic instability of a gravity-driven flow down an inclined plane is investigated in the presence of a floating elastic plate which rests on the top surface of the flow. Linear instability of the system with respect to infinitesimal disturbances is captured using normal-mode analysis. The critical conditions for instability are obtained analytically utilizing the long-wave approximation and small film aspect ratio. Further, the bifurcation of the nonlinear evolution equation is analyzed using weakly nonlinear stability analysis. The Orr-Sommerfeld system for the perturbed flow is derived, and it is solved numerically using the spectral collocation method. The behaviour of the marginal stability curves and temporal growth of the unstable waves are portrayed for a range of dimensionless flow parameters. Moreover, the pressure acting on the surface and shearing stress are calculated and analysed for various structural and flow configurations. The study reveals that critical structural parameters such as rigidity and mass per unit length play a crucial role in suppressing and facilitating the unstable surface waves of the flow. Numerical observations imply that the floating elastic plate helps to stabilize the surface flow and to damp the high amplitude waves.
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