2023/03/21 by Samer Israwi, Israwi, Samer, Youssef Khalifeh +3 · 1 citation
Earth and Planetary Sciences · #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Ocean Waves and Remote Sensing #Tropical and Extratropical Cyclones Research
paper · pdf · doi:10.48550/arxiv.2303.11556
openalex publication_date 2023/03/21 · openalex created_date 2023/03/23 · openalex updated_date 2026/07/28
A generalized version of the abcd-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and enables the description of water waves in closed basins with well-justified slip-wall boundary conditions. The derived systems possess a form that ensures their solutions adhere to important principles of physics and mathematics. By demonstrating their consistency with the Euler equations and estimating their approximation error, we establish the validity of these new systems. Their derivation is based on the assumption of small bathymetric variations. With practical applications in mind, we assess the effectiveness of some of these new systems through comparisons with standard benchmarks. The results indicate that the assumptions made during the derivation are not overly restrictive. The applications of the new systems encompass a wide range of scenarios, including the study of tsunamis, tidal waves, and waves in ports and lakes.