Influence of second-order random wave kinematics on the design loads of offshore wind turbine support structures

• Fast computation of nonlinear wave surface kinematics without use of geometric stretching.
• Cut-off frequency selection based on the limiting kurtosis of the non-Gaussian wave process.
• Coupled aero-hydro-elastic simulations reveal effect of phase differences between rotor loads and wave loads.
• Increased extreme overturning loads at the mud line with nonlinear waves.
• Effect of ocean currents on fatigue design moments.

The impact of wave model nonlinearities on the design loads of wind turbine monopile foundations is delineated based on a second-order nonlinear random wave model that satisfies the boundary conditions at the free surface and by including the effects of convective acceleration in the inertial loads. The second-order nonlinear water kinematics is developed based on a Gram Charlier series expansion using the first four stochastic moments of the wave process. The wave surface velocities and accelerations are expressed using a Taylor series expansion about the mean sea level, which satisfies to the second-order, the unsteady Bernoulli equation and normal flow condition at the free surface. The operating design loads on the monopile are computed using fully coupled and uncoupled methods. The computation of the mud level loads based on the inclusion of nonlinear wave surface kinematics is compared with those obtained when using linear waves and Wheeler stretching. The effect of the spatial derivatives of the wave velocity on the wave surface kinematics is quantified and shown to determine the wave spectral cut-off frequency limit. The spatial derivatives of wave velocity also participate in the expression for the wave convective acceleration, whose effect is demonstrated on the inertial loads on the foundation in the presence of ocean currents. The effect of nonlinear water kinematics on the monopile design load reveals the large frequency bandwidth of wave structure interaction, but the phase differences between the hydrodynamic loads with the rotor loads tend to lower the probability of joint simultaneous extreme peaks in hydrodynamics and rotor loads.