Higher-harmonic radiation loads and wave fields from instantaneous wetted surface modelling: A time-domain Rankine source study of floating wind platforms

Abstract. This study investigates how the instantaneous wetted surface affects hydrodynamic radiation loads and wave fields of floating offshore wind platforms. A direct time-domain Rankine source boundary element method compares a linear formulation evaluated at the mean body position with a body-exact formulation that updates the wetted body surface and free surface intersection at each time step. The free surface boundary conditions remain linearised about the mean water level in both cases, so differences in their responses relate to the treatment of the instantaneous wetted surface. Radiation problems are considered for a vertical cylinder as a reference geometry, as well as for the OC3-Hywind spar buoy and UMaine VolturnUS-S semi-submersible in surge, heave, and pitch motion. The unsteady pressure loads contain higher-harmonic contributions absent in the linear formulation, following a symmetry-dependent structure for the axisymmetric cylinder and spar, with a leading second harmonic in heave and leading third harmonics in surge and pitch motion. These scale with the square and the cube of the motion amplitude, respectively, and the unsteady pressure contribution to the second harmonic in heave of the spar buoy reaches 99–126 % of the linear fundamental at the largest motion amplitude for the investigated wave numbers. Including the quadratic term in Bernoulli’s equation reduces the total second harmonic to 56–73 % of the fundamental for the same cases. For the spar, the radiated wave field shows corresponding higher-harmonic content. For the non-axisymmetric VolturnUS-S, the unsteady pressure second harmonic reaches 3.7 % of the fundamental in surge, 18 % in heave, and 19 % in pitch. For the axisymmetric geometries, the second-harmonic contributions of the quadratic term vanish in surge and pitch due to symmetry. The quadratic term in Bernoulli’s equation differs only slightly between the linear and body-exact formulations but is not negligible, as it acts nearly out of phase with the unsteady pressure second harmonic. The results show that the instantaneous wetted geometry with linearised free surface boundary conditions introduces symmetry-dependent higher-harmonic radiation loads. The body-exact formulation provides a basis for further development of accelerated weak-scatterer simulations coupled with flexible structural models for the hydroelastic analysis of floating offshore wind platforms.