Variational Boussinesq model for kinematics calculation of surface gravity waves over bathymetry

Abstract Many of the widely used models for description nonlinear surface gravity waves, in deep or shallow water, such as High Order Spectral Method (HOSM) and Boussinesq-type equations, rely on elimination vertical coordinate from basic three-dimensional Euler equations. From a numerical point view are often computationally efficient, which is one main reasons that many frequently studies waves. While surface-based provide time-evolution quantities, typically elevation ? velocity potential at ? , they do not directly water particle kinematics fluid interior. However, practical applications information about water-particle crucial. The present paper presents new method calculation kinematics, quantities. presented methodology non-perturbative approach based fully Variational Boussinesq model, can be applied to wave propagation over both constant variable depth. proposed validated several cases, including Stokes solitary wave, irregular waves flat bottom. We have carried out laboratory experiments regular shoal with measurements horizontal specifically taken validation method. also employ recent statistical properties long crested propagating shoal.