2-DIMENSIONAL PARABOLIC MODELING OF EXTENDED BOUSSINESQ EQUATIONS

A frequency domain wave transformation model is derived from a set of time-dependent extended Boussinesq equations. In contrast to an earlie r study, this model is derived directly from the (eta, u) form of the equations. The resulting model maintains the excellent dispersive prop erties of the original equations and also accurately mimics the shoali ng behavior of dispersive linear theory for a wide range of water dept hs. The model is formulated in terms of a free parameter that can be t uned for optimum shoaling behavior. We tune the parameter in two ways; the first seeks the minimum error for the shoaling parameter while us ing the optimum value for the dispersion parameter, while the second s eeks the minimum combined error for both dispersion and shoaling. Thes e lead to two different sets of free parameters, with the second metho d leading to more favorable linear shoaling behavior than the first. T he effectiveness of the linear terms of the model is demonstrated by u sing them, with both sets of free parameters, to propagate waves over a shoal; comparisons to both experimental data and a linear mild-slope parabolic model are performed, and agreement is favorable for both se ts of parameters. The full model, with nonlinear terms and both sets o f parameters, is then used to simulate a laboratory experiment involvi ng harmonic generation and nonlinear wave focusing. Results indicate t hat the model can reproduce the characteristics of a lowest-order Kado mtsev-Petviashvili (KP) model in shallow water. The model also shows i mproved agreement with data relative to the KP model and another dispe rsive frequency-domain model in intermediate water depth. Additionally , there is little difference between the results from either set of pa rameters used in the model, indicating that for these cases it is not clear which optimization is most ideal.