Year: 2025
Type: article
Abstract: A complete three-dimensional long-wave polar–Cartesian equation is developed in the frequency domain. This development employs an auxiliary axis system oriented locally in the bottom gradient direction. The long-wave limit of the two-dimensional polar–Cartesian steep-slope equation is also derived. An approximate explicit expression of the coefficients is developed without restrictions on bed steepness. This is achieved by utilising a rational function approximation of the $\arctan$ function, which arises from the formulation of the vertical profile of the flow parameters. Additionally, long-wave equations in both two and three dimensions are developed in the time domain. Simulations of the long-wave equations are compared with those of the extended shallow-water equation for two-dimensional test cases, as well as for the quasi-three-dimensional scenario of oblique incidence. Our equations exhibit better agreement with the exact solutions in the majority of the test cases.
Source: Journal of Fluid Mechanics
DOI: 10.1017/jfm.2025.303
Author: Rafael Schwartz
Institution: Ariel University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4409891385