A general theory of three-dimensional wave groups Part I: The formal derivation

✍ Scribed by Paolo Boccotti

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 716 KB
• Volume: 24
• Category: Article
• ISSN: 0029-8018
• DOI: 10.1016/s0029-8018(96)00013-3

✦ Synopsis

Absl~et--If we know that a wave of given exceptionally large crest-to-~ough height occurs at a fixed point x_o at an instant to in a random wind-generated sea state, we can predict what happens with a very high probability before and after to in an area surrounding x o. The expressions of the surface displacement and velocity potential in this area are obtained in closed form. They are exact to the first order in a Stokes expansion and hold for nearly arbitrary bandwidth and solid boundary. It will be shown in Part II that these expressions represent either the evolution of a single threedimensional wave group or the collision of two wave groups, according to the configuration of the solid boundary. The theory was developed in a series of papers starting on 1981. This paper presents the whole theory in a compact form thanks to a radical simplification of the mathematical proof.