FULLY NONLINEAR PROPERTIES OF PERIODIC WAVES SHOALING OVER SLOPES

Abstract

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 (K,, c, H/h, kH, rjm, 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.