均匀流中物体引起的非线性弯曲重力波
Nonlinear flexural-gravity waves due to a body submerged in the uniform stream
摘要：
研究了弹性板下物体定常绕流的二维非线性问题。该数学模型是基于速度势理论与完全非线性边界条件的流体边界和弹性片，这是耦合在整个数值过程。采用积分速端图方法，导出了包含界面速度幅值的显式复速度势。耦合问题已减少到一个系统的非线性方程组的未知的大小的速度在界面上，这是使用配置法求解。案例研究进行亚临界和超临界流动制度。界面形状，弯矩和压力分布的结果提出了广泛的弗劳德数和淹没深度的范围。根据色散方程，界面上可能存在两个波。第一个最长的波是由重力引起的，第二个较短的波是由弹性片引起的。所得到的解决方案表现出强烈的非线性相互作用，这些波以上的潜体。结果发现，在临界弗劳德数附近，存在一个淹没范围，在该范围内的解决方案不收敛。
英文摘要：
The two-dimensional nonlinear problem of steady flow past a body submerged beneath an elastic sheet is considered. The mathematical model is based on the velocity potential theory with fully nonlinear boundary conditions on the fluid boundary and on the elastic sheet, which are coupled throughout the numerical procedure. The integral hodograph method is employed to derive the complex velocity potential of the flow which contains the velocity magnitude on the interface in explicit form. The coupled problem has been reduced to a system of nonlinear equations with respect to the unknown magnitude of the velocity on the interface, which is solved using a collocation method. Case studies are undertaken for both subcritical and supercritical flow regimes. Results for interface shape, bending moment and pressure distribution are presented for the wide ranges of Froude numbers and depths of submergence. According to the dispersion equation, two waves on the interface may exist. The first, longest wave is that caused by gravity, and the second, shorter wave is that caused by the elastic sheet. The obtained solution exhibits strongly nonlinear interaction of these waves above the submerged body. It is found that near the critical Froude number, there is a range of submergences in which the solution does not converge.
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