Existing force models for a vertical surface-piercing cylinder require water depth integration from the seabed to the free surface to determine the total inline force. However, acquiring the full wave kinematics profiles beneath the water surface presents a significant computational task. We revisit the finite water depth version of the well-known FNV theory (Kristiansen and Faltinsen, 2017) and propose a transformed version that expresses the total force solely in terms of the fully nonlinear wave properties at the free surface. This novel Transformed-FNV (T-FNV) formulation treats the Morison inertia term exactly and approximates the remaining two convective-derivative type terms with an assumption of slowly varying kinetic energy type terms. We evaluate the accuracy of this transformation against the original formulation, using wave kinematics obtained from fully nonlinear numerical simulations. Two T-FNV formulations are proposed with different input properties required. The first formulation uses the fully nonlinear wave kinematic properties at the free surface, whereas a fully approximated T-FNV formulation requires only the nonlinear free-surface elevation time history measured or calculated at the position of the column but in its absence. Both T-FNV formulations demonstrate good accuracy for wave forces for both deep and shallow-water cases against the original FNV model. The new T-FNV formulations also show the increased role of higher harmonics in the predicted force time histories when compared to those in the free-surface displacement, and the importance of using accurate higher order harmonic wave profiles in nonlinear force calculations.

中文翻译：

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Transformed-FNV：垂直圆柱体上的波浪力 — 自由表面公式

垂直表面刺穿圆柱体的现有力模型需要从海底到自由表面的水深积分来确定总的内联力。然而，获取水面下的全波运动学剖面是一项重要的计算任务。我们重新审视了著名的 FNV 理论的有限水深版本（Kristiansen 和 Faltinsen，2017），并提出了一个转换版本，仅根据自由表面的完全非线性波浪特性来表达总力。这种新颖的 Transformed-FNV (T-FNV) 公式精确地处理 Morison 惯性项，并通过假设缓慢变化的动能类型项来近似其余两个对流导数类型项。我们使用从完全非线性数值模拟获得的波运动学来评估这种变换相对于原始公式的准确性。提出了两种具有不同输入特性要求的 T-FNV 公式。第一个公式使用自由表面处的完全非线性波运动学特性，而完全近似的 T-FNV 公式仅需要在柱位置但不存在柱的位置处测量或计算的非线性自由表面高程时间历史。与原始 FNV 模型相比，两种 T-FNV 公式都证明了深水和浅水情况下波浪力的良好准确性。新的 T-FNV 公式还表明，与自由表面位移中的高次谐波相比，高次谐波在预测力时程中的作用增强，以及在非线性力计算中使用准确的高次谐波分布的重要性。