A higher-order non-hydrostatic σ model for simulating non-linear refraction–diffraction of water waves

✍ Scribed by Chih-Chieh Young; Chin H. Wu; Wen-Cheng Liu; Jan-Tai Kuo

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 765 KB
• Volume: 56
• Category: Article
• ISSN: 0378-3839
• DOI: 10.1016/j.coastaleng.2009.05.004

✦ Synopsis

A higher-order non-hydrostatic σ model is developed to simulate non-linear refraction-diffraction of water waves. To capture non-linear (or steep) waves, a 4th-order spatial discretization is utilized to approximate the large horizontal pressure gradient. A higher-order top-layer pressure treatment is further implemented to resolve wave propagation. The model's characteristics including linear wave dispersion and non-linearity are carefully examined. The accuracy of the present model using only two vertical layers is validated by laboratory data and the available results predicted by the non-linear Schrödinger equation, Boussinesq-type equations, the non-linear mild slope equation, and the Laplace equation. Features of harmonic generation as well as the influences of dispersion and non-linearity on wave energy transfer processes are discussed.