We investigate the harmonic structure of wave-induced loads on vertical cylinders with dimensions comparable to those used to support offshore wind turbines. Many offshore wind turbines are designed, so the structural resonance is two or three times the fundamental wave loading period, which may be excited by higher harmonics of wave loading. The suitability of a "Stokes-type' model for force is examined. We analyse experimental data for unidirectional and directionally spread sea-states. We demonstrate that approximate harmonic components may be extracted from a random time series, using a novel signal processing method. The extracted harmonics are shown to follow a "Stokes-like' model, where the higher harmonics in frequency are proportional to the n-th power of the linear inline force component and its Hilbert transform. Results show that the third harmonic component of force is fitted less well by this model, which is consistent with the literature. A key new result is that the harmonic coefficients for spread and unidirectional seas are nearly identical when fitted as powers of the linear inline force and its Hilbert transform. This finding has the potential to greatly simplify the process of generating harmonic data for new wavelength to cylinder and wavelength to depth ratios. This also implies that the size of the inline component of the nth harmonic for force in a directional sea relative to the same component in a unidirectional sea scales as cos(n) sigma(theta), where sigma(theta) is the rms directional spreading angle of the incident wave field. Hence, higher harmonics will be of less importance in directionally spread seas than unidirectional ones. We show that the computationally fast harmonic decomposition approach taken here can reproduce the shape and magnitude of the loading from non-breaking waves waves in a wide range of realistic unidirectional and directionally spread sea-states. The proposed force model has potential as an engineering tool for computationally fast prediction of nonlinear wave loads.
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