Abstract The parametric resonance in roll motion (known shortly as parametric roll) was studied for a fishing vessel in regular waves. This is an instability and resonance phenomenon that can lead the roll to reach very high oscillation amplitudes at its natural frequency, depending on the damping level involved. In the worst cases it is responsible for vessel capsize. Here the problem was investigated numerically and experimentally, performing dedicated physical tests on a typical Norwegian fishing vessel with blunt hull and small length-to-beam ratio. Experimentally, a dedicated study was carried out on the SFH112 fishing vessel in scale 1:10 in regular head-sea waves with different wave frequencies and steepnesses. The tests were performed without and with forward speed, with corresponding Froude number Fn = 0.09 and 0.18. Numerically, a blended method was developed based on a 6-DOF 3D hybrid method where the radiation and diffraction potentials were computed for zero forward speed by WAMIT and used in the STF strip theory to obtain speed dependent loads. The convolution integrals were used to account for the effect of radiation free-surface memory effect. Nonlinearities in the Froude-Krylov and restoring loads were accounted for by integrating the corresponding pressure terms on the instantaneous wetted-hull surface defined by the incident waves and body motions. Use of the weak-scatterer hypothesis in radiation and diffraction loads has also been considered. The method was applied to reproduce and complement the experiments on the SFH112 fishing vessel. The numerical simulations showed good agreement with the experimental results. For the cases near the instability border of a 1-DOF Mathieu-type instability diagram, the physical and numerical predictions were different in terms of parametric roll occurrence. The instability borders for the experimental cases are also different from the instability borders of 1-DOF Mathieu-type instability diagram. The instability region for the experiments and 6DOF simulations cover a wider range of frequency ratio and the threshold value of metacentric height variation amplitude to have parametric roll seems to be lower than predicted by the 1-DOF Mathieu instability diagram. The results also show that the instability region for the cases with forward speed shifts to the lower frequency ratios(natural roll frequency to encounter frequency ratio) compared to the cases without forward speed. The effect of the weak-scatterer hypothesis on the results is also assessed and shown to be important for parametric roll. The results show that the simulations without this hypothesis tend to underestimate the occurrence and severity of parametric roll especially in longer and steeper waves.

中文翻译：

---

渔船有无前进速度参数横摇共振的数值与实验研究

摘要 研究了一艘渔船在规则波浪中横摇运动中的参数共振（简称参数横摇）。这是一种不稳定和共振现象，会导致轧辊在其固有频率下达到非常高的振荡幅度，具体取决于所涉及的阻尼水平。在最坏的情况下，它负责船舶倾覆。在这里，对问题进行了数值和实验研究，对一艘典型的挪威渔船进行了专门的物理测试，该渔船具有钝船体和小长梁比。在实验上，对 SFH112 渔船以 1:10 的比例在具有不同波浪频率和陡度的常规逆海波浪中进行了专门研究。测试在没有和有前进速度的情况下进行，相应的弗劳德数 Fn = 0.09 和 0.18。数字上，基于 6-DOF 3D 混合方法开发了一种混合方法，其中 WAMIT 计算了零前进速度的辐射和衍射势，并用于 STF 条带理论以获得与速度相关的载荷。卷积积分用于解释辐射自由表面记忆效应的影响。Froude-Krylov 和恢复载荷中的非线性是通过对由入射波和身体运动定义的瞬时湿船体表面上的相应压力项进行积分来计算的。还考虑在辐射和衍射负载中使用弱散射体假设。该方法用于在 SFH112 渔船上重现和补充实验。数值模拟与实验结果吻合良好。对于 1-DOF Mathieu 型失稳图的失稳边界附近的情况，物理和数值预测在参数侧倾发生方面是不同的。实验案例的不稳定边界也不同于1-DOF Mathieu型不稳定图的不稳定边界。实验和 6DOF 模拟的不稳定区域覆盖了更宽的频率比范围，具有参数横滚的偏心高度变化幅度的阈值似乎低于 1-DOF Mathieu 不稳定图的预测。结果还表明，与没有前进速度的情况相比，有前进速度的情况下的不稳定区域转移到较低的频率比（自然侧倾频率与遭遇频率之比）。还评估了弱散射体假设对结果的影响，并表明这对参数滚转很重要。结果表明，没有这个假设的模拟往往会低估参数横摇的发生和严重程度，尤其是在更长和更陡峭的波浪中。