| Summary: | 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 & Faltinsen,
2017, Journal of Fluid Mechanics, 833, 773–805) 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 freesurface 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.
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