A class of exact, time-dependent, free-surface flows
A class of exact, time-dependent, free-surface flows
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一类精确的、随时间变化的自由表面流
DOI：
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发表时间：
1972
影响因子：
3.7
通讯作者：
M. Longuet
中科院分区：
文献类型：
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作者：
M. Longuet
注意一类无粘无旋流，满足条件，在一个时间依赖的自由表面。这些流动与狄利克雷（1860）的椭球有关。根据参数P，横截面可以采取可变椭圆（P < 0）、双曲线（P > 0）或一对平行线（P = 0）的形式。Taylor（1960）从理论和实验两方面研究了椭圆情况。双曲线情况（P > 0）是值得注意的，因为当渐近线之间的角度接近直角时，流动发展为奇点。有人建议，这种解决方案代表了一个可能的不稳定性附近的大振幅的重力驻波的波峰。在中间的情况下（P = 0）的解决方案描述了一个开放的通道流，其中的流体丝均匀地拉伸在水平方向上。后一种流动是实验证明的。
Attention is drawn to a class of inviscid irrotational flows which satisfy the conditions at a time-dependent free surface exactly. The flows are related to the ellipsoids of Dirichlet (1860). Depending on a parameter P, the cross-section may take the form of a variable ellipse (P < 0), a hyperbola (P > 0) or a pair of parallel lines (P = 0). The elliptical case was investigated both theoretically and experimentally by Taylor (1960). The hyperbolic case (P > 0) is remarkable in that the flow develops a singularity when the angle between the asymptotes approaches a right-angle. It is suggested that this solution represents a possible instability near the crest of a standing gravity wave of large amplitude. In the intermediate case (P = 0) the solution describes an open-channel flow in which the fluid filaments are stretched uniformly in a horizontal direction. The latter flow is demonstrated experimentally.