In this chapter the wave body interaction is extended to the second order in the wave amplitude. This leads to wave loads, and responses, taking place at the sum and difference frequencies of the components in the incoming wave system. The time averaged wave load (the drift force) is first considered in regular waves. The different formulations of the drift force (near-field, far-field, middle-field, Lagally) are described. The sensitivity of the drift force to a coincident current is emphasized and the extension of the diffraction radiation theory to a superimposed current is presented, together with the so-called Aranha’s formula that offers a practical approximation to the wave drift damping effect. Second-order diffraction theory is detailed in regular waves, with practical application to a bottom-mounted vertical cylinder. The concept of Quadratic Transfer Function (QTF) is first introduced in the case of bichromatic seas and then applied to the low frequency loading in irregular waves, where the validity of frequently used approximations (e.g. Newman approximation) is discussed. A section is then devoted to the Rainey equations which can be viewed as a second-order extension of the inertia term in the Morison equation. Finally practical calculation of the slow-drift and springing responses is considered.

In this chapter linearized potential flow theory is applied to the prediction of wave loads upon marine structures, and of their wave response. The linearized diffraction radiation theory is presented, leading to the wave excitation loads, added masses, and radiation dampings. Analytical, semi-analytical, and numerical methods of resolution are given, the first one for the case of one or several bottom-mounted vertical cylinders. Comparisons are offered with experimental results, where the merits and short-comings of the linearized theory are emphasized. Separate sections are then devoted to specific problems such as barge roll resonance, recovery of wave energy, coupling between seakeeping and sloshing in tanks, and resonances in moonpools and gaps.