Fully nonlinear properties of periodic waves shoaling over slopes
Date of Original Version
Shoaling of finite amplitude periodic waves over a sloping bottom is calculated in a numerical wave tank which combines: (i) a Boundary Element Model to solve Fully Nonlinear Potential Flow (FNPF) equations; (ii) an exact generation of zero-mass-flux Streamfunction Waves at the deeper water extremity; and (iii) an Absorbing Beach (AB) at the far end of the tank, which features both free surface absorption (through applying an external pressure) and lateral active absorption (using a piston-like condition). A feedback mechanism adaptively calibrates the beach absorption coefficient, as a function of time, to absorb the period-averaged energy of incident waves. Shoaling of periodic waves of various heights and periods is modeled over 1:35, 1:50, and 1:70 slopes (both plane and natural), up to very close to the breaking point. Due to the low reflection from both the slope and the AB, a quasi-steady state is soon reached in the tank for which local and integral properties of shoaling waves are calculated (Ks, c, H/h, kH, ηm, Sxx, ...). Comparisons are made with classical wave theories and observed differences are discussed. Parameters providing an almost one-to-one relationship with relative depth kh in the shoaling region are identified. These could be used to solve the so-called depth-inversion problem.
Proceedings of the Coastal Engineering Conference
Grilli, Stéphan T., and Juan Horrillo. "Fully nonlinear properties of periodic waves shoaling over slopes." Proceedings of the Coastal Engineering Conference 1, (1997): 717-730. doi:10.1061/9780784402429.057.