ABSTRACT
Surface gravity waves on deep water are necessarily dispersive [1]; as a result, they tend to travel in groups when their wave lengths differ little. The ubiquity of wave groupiness is reflected in the folklore that “every seventh wave is the largest.” It is also known [2] that such waves once generated, e.g., by a storm, propagate thousands of miles across the ocean without significant dissipation and their propagation is well described by the inviscid irrotational flow theory in hydrogynamics. During the propagation, while dissipation is negligible, the nonlinear self-interaction among waves in a group, i.e., waves having more or less the same wave length, can be very important, resulting in the gradual but significant evolution of the waves themselves and their group shape. This paper studies the three-dimensional properties of such nonlinear interactions and some of their applications.
