Phase‐Resolving Wave Modeling

Abstract

Phase‐resolving modeling of sea waves is the mathematical modeling of surface waves including explicit reproduction of the sea surface and velocity field evolution. The general approach is based on equation of potential motion with a free boundary. Conformal transformation of coordinates is the most effective method of solution of two‐dimensional ( x–z ) periodic problem. For three dimensional models, several different approaches have been developed: boundary integral equation method (BIEM), method based on expansion of velocity potential in a vicinity of surface [high order spectral method (HOSM)], and method based on direct solution of three‐dimensional equation for velocity potential. These methods do not compete with each other because all of them have their advantages. The brief descriptions of each method are given as well as the examples of theirs applications. The investigations of nonperiodic problems are based on a direct solution of equation for velocity potential. The methods of including in the models of algorithms for parameterization of energy input and dissipation are discussed.