The second order low-frequency loads are one of main sources of excitation for moored systems. These loads are usually decomposed into the quadratic part, contributed only by first order quantities and potential part contributed by the second order potentials. In shallow water the second order incoming and diffracted potentials give a significant contribution to the low frequency forces. Therefore, the accuracy on the determination of this parcel of the low-frequency loads is a key issue for the assessment of mooring lines and operability of systems moored in shallow water area, as for example LNG terminals.
Due to the complexity in computing the second order diffraction potential, which would involve a non-homogeneous free surface boundary condition, the so-called Pinkster approximation has been proposed. This approximation is based on the assumption that the major contribution to the potential part of low-frequency loads is given by the second order potential of the undisturbed incoming waves. The methods to compute the wave forces related to the second order potentials are based on scaling of the first order wave induced forces.
Another approximation recently formulated in Chen and Rezende consists of developing the second-order bi-frequency load into a series of different orders of the difference frequency. The potential contribution to the term proportional to the difference-frequency can be evaluated efficiently by involving an integral over a small zone on the free surface around the body.
In the present paper, the existing approximations are revisited and compared to analytical solution of exact second-order load on a vertical cylinder and for the case of floating body (LNG) in shallow water. Some guidelines in the practical use of different approximations will be derived.