Free surface flow past topography: A beyond-all-orders approach
Free surface flow past topography: A beyond-all-orders approach
复制标题
经过地形的自由表面流：超越所有秩序的方法
DOI：
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发表时间：
2012
影响因子：
1.9
通讯作者：
B. Binder
中科院分区：
文献类型：
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作者：
C. Lustri;S. McCue;B. Binder
本文研究了亚临界自由面定常绕流淹没斜台阶的问题。讨论了小佛汝德数的渐近极限，特别强调了改变台阶面角度对表面波的影响。Chapman & Vanden-Broeck（2006）Exponential asynchronotics and gravity waves. J. Fluid Mech.567，299-326中，以弗劳德数的平方的幂为单位的幂级数展开的发散是由自由表面的解析延拓中的奇点引起的;对于倾斜台阶，这些奇点可以对应于台阶的拐角或停滞点，或者两者，这取决于倾斜角度。斯托克斯线从这些奇点发出，并且指数小波在斯托克斯线与自由表面相交的点处被打开。我们的研究结果表明，对于一定范围的步距角，两个波列被打开，但指数次显性的一个被打开第一，导致一个中间波列没有以前注意到。我们把这些想法推广到有倾斜面的淹没凸块或沟渠上的流动问题。这一次可能有两个，三个或四个有效的斯托克斯线，这取决于倾角。我们演示了如何构建一个基础地形，使波的贡献，从单独的斯托克斯线是相同的幅度，但相反的相位，从而抵消了。我们的渐近结果的补充完全非线性方程的数值解。
The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck, (2006) Exponential asymptotics and gravity waves. J. Fluid Mech.567, 299–326, the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of inclination. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.