Work

Rigid lid limit in shallow water over a flat bottom

Year: 2024

Type: article

Abstract: We perform the so‐called rigid lid limit on different shallow water models such as the abcd Bousssinesq systems or the Green–Naghdi equations. To do so, we consider an appropriate nondimensionalization of these models where two small parameters are involved: the shallowness parameter and a parameter which can be interpreted as a Froude number. When the parameter tends to zero, the surface deformation formally goes to the rest state, hence the name rigid lid limit. We carefully study this limit for different topologies. We also provide rates of convergence with respect to and careful attention is given to the dependence on the shallowness parameter .

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.12773

Author: Benjamin Melinand

Institutions: Centre National de la Recherche Scientifique, Centre de Recherche en Mathématiques de la Décision, Université Paris Sciences et Lettres, Université Paris Dauphine-PSL

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: $4,330

Funder: Agence Nationale de la Recherche