Improved Boussinesq-type equations for flexural-gravity waves
Year: 2025
Type: article
Abstract: The Boussinesq approximations have been employed to investigate flexural-gravity waves in shallow water, with Boussinesq-type equations derived concerning depth-averaged horizontal velocity. In this paper, we derive improved Boussinesq-type equations utilizing the velocity at an optimized elevation as the primary variable, while considering variations in plate stiffness and bathymetry. These new equations are applicable to greater depths than the shallow water Boussinesq-type equations, significantly improving the linear dispersion relation. A numerical solver is also developed to solve the improved equations, employing a fourth-order Adams–Bashforth–Moulton scheme for temporal advancement and a finite difference scheme for spatial discretization. The inertial term associated with the second-order time derivative and the elastic term associated with the fifth-order spatial derivative in the improved equations are addressed in the numerical scheme. Both the regular and solitary waves are computed, and the inertial effects are analyzed. Variations in plate stiffness and bathymetry in the direction aligned with or perpendicular to the wave direction are considered, and their resultant effects on flexural-gravity waves are studied. It is discovered that the wave amplitude does not necessarily increase during wave shoaling, and variations in plate stiffness and bathymetry can lead to significant refraction of flexural-gravity waves.
Source: Physics of Fluids
DOI: 10.1063/5.0252832
Authors: Yingfen Xiong, Shanran Tang, Liangsheng Zhu
Institution: South China University of Technology
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Award: G4893510025
OpenAlex ID: W4408150645