Verification of the Benjamin–Lighthill conjecture about steady water waves
Verification of the Benjamin–Lighthill conjecture about steady water waves
复制标题
关于稳定水波的本杰明-莱特希尔猜想的验证
DOI：
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发表时间：
1995
影响因子：
3.7
通讯作者：
T. Benjamin
中科院分区：
文献类型：
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作者：
T. Benjamin
为了证实Benjamin和Lighthill（1954）提出的一个一般性质，重新考虑了水平底上方理想液体表面上的定常周期波（Stokes波）的精确问题。具体地说，在参数r和s分别成比例的总水头和流力常数的稳定流，这样的波被证明实现点（r，s）内的区域的（r，s）的平面是由尖点曲线表示所有可能的均匀流。一个相应的属性，稳定的周期波的表面上的一个无限深的理想液体也将被证明。最后的讨论涉及到非周期性斯托克斯波的定常水波，并参考附录B对定常波问题的哈密顿表述中的流力不变量s的重要性进行了评论。
The exact problem of steady periodic waves (Stokes waves) on the surface of an ideal liquid above a horizontal bottom is reconsidered in order to confirm a general property conjectured by Benjamin & Lighthill (1954). Specifically, in terms of parameters r and s proportional respectively to the total-head and flow-force constants for steady flows, such waves are proved to realize points (r, s) inside the region of the (r, s)-plane that is bounded by the cusped curve representing all possible uniform streams. A corresponding attribute of steady periodic waves on the surface of an infinitely deep ideal liquid will also be demonstrated. The concluding discussion refers to steady water waves that are not periodic Stokes waves, and comments with reference to Appendix B on the significance of the flow-force invariant s in Hamiltonian representations of the steady-wave problem.