Transformed-FNV: Wave forces on a vertical cylinder — A free-surface formulation

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.