Parabolic Mild Slope Wave Model

The Parabolic Mild Slope Wave Model Module is a linear wave refraction–diffraction model based on a parabolic approximation of the elliptic mild-slope equation. This module simulates the effects of wave refraction and shoaling caused by depth variations, as well as wave energy dissipation due to bottom friction and wave breaking. It can also represent the effects of frequency spreading and directional spreading by applying the principle of linear superposition.

This wave module is based on equations derived from the parabolic approximation of the mild-slope equation. Several parabolic approaches can be applied, ranging from a simple approximation for small wave angles to more advanced formulations for larger wave angles, up to approximately 60°. The parabolic equation is solved using a Crank–Nicolson finite difference scheme.

The module is well suited for studying wave disturbances in open coastal waters, including open coastlines with coastal structures such as breakwaters, wave barriers, and similar structures. It is most appropriate when reflected waves from coastal structures can be neglected and when wave diffraction mainly occurs in the principal wave direction. This module is particularly important for analyzing wave conditions, including wave height, wave period, and wave direction, as well as wave-induced currents. These parameters are essential for sediment transport studies and for assessing erosion and deposition patterns in coastal zones.

However, this module is not fully suitable for detailed studies of wave refraction and diffraction in complex harbor areas with many coastal structures. It may still be used to support assessments of the strength and stability of harbor structures, but it is not intended to evaluate the effects of wave refraction and diffraction on vessel stability or ship maneuvering inside harbors.