Abstract A nonlinear time-domain numerical model based on a body-exact approach is applied to study the problem of large amplitude motion of a tightly moored submerged sphere. In this model, the exact body condition on the instantaneous wetted body surface is satisfied as well as the linear condition on the still water surface. Numerical simulations were carried out for two wave steepness, each with various incident wave frequencies. It was found that for a smaller wave steepness, the oscillation frequency of the sphere is always the same as the wave frequency, while for a larger steepness, the sphere may oscillate with a large amplitude at the frequency that is half of the incident waves. The linear model satisfying both the linearized boundary conditions on the mean body surface and still water surface fails to capture this significant nonlinear phenomenon. This phenomenon is induced by a self-amplifying process in which the wave frequency potential and half-wave frequency body motion generate a half-wave frequency nonlinear wave force, while the half-frequency force in turn enhances the half-wave frequency motion.

中文翻译：

---

单色波作用下紧密系泊水下球体的半波频率响应现象，采用体精确法模拟

摘要 应用基于身体精确法的非线性时域数值模型研究紧系泊水下球体的大振幅运动问题。在该模型中，满足瞬时润湿体表面的精确体条件以及静水表面的线性条件。对两个波陡度进行了数值模拟，每个波陡度都有不同的入射波频率。发现对于较小的波陡度，球体的振荡频率总是与波频率相同，而对于较大的波陡度，球体可能在入射波频率的一半处以较大的幅度振荡。满足平均体表面和静水表面线性化边界条件的线性模型未能捕捉到这种显着的非线性现象。这种现象是由波频势和半波频体运动产生半波频非线性波力，而半频力又增强半波频运动的自放大过程引起的。