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