Planing hull dynamics in water waves: Physical insights from nonlinear strip theory models and fully nonlinear computational fluid dynamics simulations

The dynamic motions of planing hulls in water waves represent a well-known example of a strongly nonlinear fluid-structure interaction problem, where wave-induced motions are governed by intermittent contact, spray formation, transom wake flow, and higher-harmonic responses. In this study, nonlinear strip theory models, namely, two-dimensional plus time ( 2 D + t ) models, extending classical strip theory formulations by incorporating nonlinear wave kinematics and an improved analytical water-entry solution that captures nonlinearity, are developed alongside a fully nonlinear computational fluid dynamics (CFD) model based on a Reynolds-averaged Navier-Stokes solver. These models are employed to investigate the physics of nonlinear unsteady planing motions under different wave conditions. Results show that the second harmonic of the heave motion tends to increase with wave steepness, whereas that of the pitch motion may decrease due to the onset of airborne phases. The higher harmonics of heave and pitch in short waves are primarily caused by intermittent wetted-surface variations and wave scattering, the latter introducing irregularities in the response that are absent in the 2 D + t model. At intermediate wavelengths, nonlinearities arise mainly from airborne motion and subsequent slamming impacts, while at long-wave conditions, additional effects, including water detachment and subsurface vorticity generation, contribute to the nonlinear response, phenomena captured only by the CFD simulations. Consequently, the response amplitude operators of heave and pitch are seen to increase with wave steepness in long-wave conditions when computed using the CFD model. This distinction highlights that, although the second-order and earlier 2 D + t formulations remain valuable predictive tools, they cannot fully reproduce the nonlinear behavior observed in steep-wave regimes. Specifically, they can have application in the early-stage design, rapid parametric studies for physical studies, and long-duration simulations due to its low computational cost and clear physical interpretability.