A discussion on the second-order wave forces and wave drift damping

In this paper we derive a formulation for the second-order wave drift force on an object sailing at low forward speed. The method used consists of the application of the law of conservation of impulse over the fluid domain outside the body. We are interested in the large second order resonant motions where the damping coefficients in the equation of motion are mainly determined by the influence of the motion on the mean drift force at the frequency of excitation. The results are compared with results obtained by the direct pressure integration method. Due to the small first order damping at small frequencies the second order wave drift damping becomes significant. We present a formulation for this coefficient based on the speed dependency of the wave drift force. It is shown that an approximate formulation of Aranha gives reasonable results in some cases. However, it leads to large errors in the case that the first order motions are near resonance.