We present some explicit solutions (given in Eulerian coordinates) to the three-dimensional nonlinear water wave problem. The velocity field of some of the solutions exhibits a non-constant vorticity vector. An added bonus of the solutions we find is the possibility of incorporating a variable (in time and space) surface pressure which has a radial structure. A special type of radial structure of the surface pressure (of exponential type) is one of the features displayed by hurricanes, cf. Overland (Earle, Malahoff (eds) Overland in ocean wave climate, Plenum Pub. Corp., New York, 1979).

中文翻译：

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三维非线性水波问题的一些显式解

我们为三维非线性水波问题提出了一些明确的解决方案（以欧拉坐标给出）。一些解的速度场表现出非常量的涡量矢量。我们发现的解决方案的另一个好处是可以结合具有径向结构的可变（时间和空间）表面压力。一种特殊类型的表面压力径向结构（指数型）是飓风显示的特征之一，参见。Overland (Earle, Malahoff (eds) Overland in sea wave climate, Plenum Pub. Corp., New York, 1979)。