Second-order low-frequency drift motions of a floating body calculated by different approximation methods

Abstract

The paper presents an experimental and numerical investigation of the low-frequency motions of a simple geometry floater subjected to bichromatic waves and to long crested irregular seas. The body is axis-symmetric about the vertical axis and it is restrained from drifting away by a linear mooring system. The investigation is carried out for three water depths representing deep water, intermediate water depth and shallow water. The objective is to assess the water depth influence on the second-order low-frequency motions. A second objective is to assess the results of different approximations for the second-order difference frequency wave exciting forces on the second-order motions. The quadratic transfer functions are calculated with a boundary element method using several levels of approximation for the second-order forces: (a) the most complete approximation solves the boundary value problem completely up to the second order, (b) the first-order approximation neglects the free surface forcing in the 2nd order boundary value problem solution, (c) Newman’s approximation is of zeroth-order with respect to the difference frequency, (d) a fourth method combines Newman’s approximation with a contribution from the second-order incident wave potential, (e) the fifth method is applied to the heave forces only and it combines Newman’s approximation corrected by an additional set down. This study shows that the contribution from the second-order velocity potential must be considered for shallow water calculations to achieve accurate results. For small difference frequencies, second-order scattering potential effects are small; therefore, in this case, a good practical approximation consists on considering the second-order potential is contributed by the incident waves only.