Fully Nonlinear Properties of Periodic Waves Shoaling over Slopes

Proc. 25th Intl. Conference on Coastal Engineering (ICCE25, Orlando, 9/96),  Vol. 1, pps. 717-730. ASCE Edition, 1997.

Stephan T. Grilli                         and                   Juan Horrillo

Associate Professor                                           Graduate student
Department of Ocean Eng.                                           
niversity of Rhode Island                                    
Narragansett, RI 02882, USA                            

Abstract :  

Shoaling of finite amplitude periodic waves over a sloping bottom is calculated in a {\em numerical wave tank} which combines : (i) a Boundary Element Model to solve Fully Nonlinear Potential Flow (FNPF) equations; (ii) an exact generation of {\em 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.

\noindent 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, MWL, 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.

Keywords :

Nonlinear wave modeling, streamfunction waves, wave generation, wave absorption, numerical wave tank, wave shoaling, Boundary Element Method

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