In 1957, Crapper found an exact solution for capillary waves in an irrotational flow of infinite depth. Here we provide asymptotic and numerical evidence that a Crapper wave makes the profile of a periodic traveling wave in a constant vorticity flow when the effects of gravity and surface tension are negligible. This is achieved by explicitly constructing successive approximate solutions for small amplitude waves and numerically computing arbitrary amplitude waves.

中文翻译：

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Crapper精确解在恒定涡流中的新应用

1957年，克雷珀（Crapper）发现了无限深非旋流中毛细波的精确解。在这里，我们提供渐近和数值证据，当重力和表面张力的影响可忽略不计时，克珀波使周期性行波的轮廓在恒定涡流中产生。这是通过显式构造小振幅波的连续近似解并通过数值计算任意振幅波来实现的。