Using a variational principle and a parabolic approximation to the vertical structure of the velocity potential, the equations of motion for surface gravity waves over mildly sloping bathymetry are derived. No approximations are made concerning the non-linearity of the waves. The resulting model equations conserve mass, momentum and positive-definite energy. They are shown to have improved frequency-dispersion characteristics, as compared to classical Boussinesq-type of wave equations.
|Number of pages||4|
|Publication status||Published - 19 May 2005|
|Event||20th International Workshop on Water Waves and Floating Bodies, IWWWFB 2005 - Longyearbyen, Norway|
Duration: 19 May 2005 → 1 Jun 2005
Conference number: 20
|Conference||20th International Workshop on Water Waves and Floating Bodies, IWWWFB 2005|
|Period||19/05/05 → 1/06/05|
Klopman, G., Dingemans, M. W., & van Groesen, B. (2005). A variational model for fully non-linear water waves of Boussinesq type. Paper presented at 20th International Workshop on Water Waves and Floating Bodies, IWWWFB 2005, Longyearbyen, Norway.