Exterior Reflections in Elliptic Harbor Wave Models

Abstract

Traditional elliptic harbor wave models are based on the assumptions that the exterior sea region (i.e. the region outside the computational grid) is of constant depth and that the exterior coastlines are collinear and fully reflecting. This paper demonstrates that for most coastal regions, where these assumptions are generally not true, their effect on model results is substantial. This leads to unreliable simulations. Enlarging the model domain to overcome their effects is cumbersome and often prohibitive. To overcome these difficulties, the use of parabolic approximations of the mild-slope wave equation as open boundary conditions is explored. Suitable parabolic equations are derived and interfaced with an elliptic finite-element model. Since the parabolic approximation does not describe wave scattering as rigorously as the traditional method, the new model is tested against analytical and other solutions for cases where scattering is extensive. Errors resulting from the parabolic approximation are found to be extremely small. Further model tests show that for the generally realistic case where exterior reflection coefficients are less than unity, the new method requires considerably smaller domains than the traditional method, resulting in reduced modeling effort. The model is also applied to Toothacher Bay, Maine, and the use of the parabolic boundary conditions eliminates many spurious features in the simulation.