On linearization of Morison force given by high three-dimensional sea wave groups

In-line loading on slender marine structures may be computed by means of the Morison equation, which includes the inertia term (depending on wave acceleration) and the drag term (depending on square velocity). In the presence of random sea waves (either two- or three-dimensional waves), the Morison equation needs a linearization in the drag term, in order to obtain the force spectrum. In this paper, the Boccotti's Quasi-Determinism theory is applied for the calculation of the drag force given by high three-dimensional wave groups. It is shown that when a crest-to-trough wave of given height H occurs on a vertical pile, the quotient between maxima of sectional drag Morison force and of force given by linearization (both calculated at a fixed depth z) is equal to C times H / H_s, where H_s is the significant wave height. The coefficient C is equal to 1.25 for narrow-band spectra, whatever be the value of z is. For the three-dimensional random wave groups it is obtained that C is equal to 1.25 for z close to 0; the value of C slightly decreases on approaching the bottom. Then, it is shown that the Borgman linearization is not conservative for the calculation of extreme drag forces in three-dimensional waves: for example the maximum drag Morison force given by a wave height H equal to 2 times H_s, is close to 2.3 times the maximum force given by linearization. The results are finally validated by the means of Monte Carlo simulations of random sea waves.