Elliptic Mild Slope Wave Model

The Elliptic Mild Slope Wave Model Module uses an efficient numerical solution of the mild-slope equation. This equation is developed from the harmonic motion of infinitesimal-height waves over a seabed with a gradually varying slope. The module incorporates linear wave refraction–diffraction equations, including the effects of wave breaking, bottom friction, and wave damping.

Partial wave refraction and transmission through piers, harbor structures, and breakwaters can also be represented. A sponge layer, or wave-absorbing layer, may be applied when a numerical solution requires wave energy absorption near the model boundaries. The module also includes numerical formulations for wave radiation stresses, which are important for analyzing wave propagation across intersecting wave fields and in areas where strong wave diffraction occurs.

The Elliptic Mild Slope Wave Model Module uses a unique numerical solution method. Harmonic time variation is extracted, and the elliptic equation is formulated as mass and momentum equations. These equations are solved using a finite difference scheme with an Alternating Direction Implicit (ADI) algorithm. Wave-period calculations are derived from wave height, particle velocity components, sea level, and especially wave breaking, which is determined from wave radiation stresses within the modeled area.

This wave model is used to study wave resonance in harbors, long-period waves, and wave forces in relatively small coastal areas where wave diffraction and wave breaking are important. The dominant wave forcing is typically monochromatic and unidirectional. The module can be applied to all seabed depth profiles, although it has limitations in representing nonlinear effects, including wave-amplitude dispersion and wave-wave interactions. This model is particularly suitable for analyzing short-period wave disturbances inside harbors.