Harmonic function expansion for translating Green functions and dissipative free-surface waves

Abstract

Three-dimensional gravity free-surface waves involving energy dissipation are examined. The singular wave integral from a non-dissipative translating Green function is approximated as a regular wave integral of a dissipative Green function. The regular wave integral method enables a dissipative free-surface wave to be derived from an expansion of whole-space harmonic functions. The new approximation technique, applicable to dissipative and non-dissipative free-surface wave problems, simplifies the numerical simulations of three-dimensional Green functions and free-surface waves.