The Effect of the Second-order Difference-frequency Wave Force on the Motions of an Underwater Vehicle Near the Surface

When an underwater vehicle performs tasks, such as power recharge, air exchange, deployment, and retrieval near the surface, the low-frequency suction force and pitch moment will interfere with its motion. This paper presents a study on the effect of second-order difference-frequency wave force on the motions of the DARPA SUBOFF model at various submergence depths and environmental conditions. Ignoring the second-order wave force component induced by the second-order differencefrequency force may underestimate the second-order effect in irregular waves in the time domain. Comparisons were made between Newman's approximation, which sets the off-diagonal difference-frequency quadratic transfer function (QTF) value to the average over the corresponding diagonal values, and the full QTFs based on the Pinkster approximation in the frequency and time domains. The QTFs-based prediction is significantly larger values than Newman's approximation. Time-domain simulations were conducted, to investigate the effect of the second-order difference-frequency wave loads on motion responses at different nondimensional submergence depths and various sea conditions. The results of the computation indicate that ignoring the second-order difference-frequency wave force may underestimate the motion and dynamic responses of underwater vehicles; in addition, the pitch and heave motion responses are dominated by the low-frequency response.