Accurate Depth Inversion Method for Coastal Bathymetry: Introduction of Water Wave HighOrder Dispersion Relation

• Main Authors: Hongli Ge, Hao Liu, Libang Zhang
• Format: Article
• Language: English
• Published: MDPI AG 2020-02-01
• Series: Journal of Marine Science and Engineering
• Subjects: fredholm’s alternative theorem; wavenumber coupling equation; highorder dispersion relation; coastal bathymetry
• Online Access: https://www.mdpi.com/2077-1312/8/3/153

This paper proposes a wave model for the depth inversion of sea bathymetry based on a new highorder dispersion relation which is more suitable for intermediate water depth. The core of this model, a highorder dispersion relation is derived in this paper. First of all, new formulations of wave over generally varying seabed topography are derived using Fredholm’s alternative theorem (FAT). In the new formulations, the governing equation is coupled with wave number and varying seabed effects. A new highorder dispersion relation can be obtained from the coupling equation. It is worth mentioning that both the slope square and curvature terms () of water wavenumber and seabed bottom are explicitly expressed in high-order dispersion relation. Therefore, the proposed method of coastal bathymetry reversion using the higherorder dispersion relation model is more accurate, efficient, and economic.