Complements of Space–Time Theory of Sea States
The chapter introduces the equations of random surface elevation η and velocity potential ϕ of a sea state interacting, respectively, with a long vertical breakwater and with a semi-infinite vertical breakwater. Then it deduces the cross-covariances of η and η, and η and ϕ, for these nonhomogeneous wave fields, as well as for the homogeneous wave field in the open sea. These cross-covariances will be employed by the quasi-determinism (QD) theory. The chapter evidences the existence of an area of the lee of vertical breakwaters wherein the diffraction coefficient is at least 50% greater than the diffraction coefficient of the periodic waves. This anomaly will be explained in Chapter 11 in light of the QD theory.