Generalised Serre–Green–Naghdi equations for open channel and for natural river hydraulics

Article type: Research Article

Authors: Debyaoui, Mohamed Ali | Ersoy, Mehmet^{; *}

Affiliations: Université de Toulon, IMATH EA 2134, 83957 La Garde, France. E-mails: Mohamed-Ali-Debyaoui@etud.univ-tln.fr, Mehmet.Ersoy@univ-tln.fr

Correspondence: [*] Corresponding author. E-mail: Mehmet.Ersoy@univ-tln.fr.

Abstract: In this paper, we present a new non-linear dispersive model for open channel and river flows. These equations are the second-order shallow water approximation of the section-averaged (three-dimensional) incompressible and irrotational Euler system. This new asymptotic model generalises the well-known one-dimensional Serre–Green–Naghdi (SGN) equations for rectangular section on uneven bottom to arbitrary channel/river section.

Keywords: Open channel flow, river flow, Euler equations, asymptotic approximation, Serre–Green–Naghdi equations, free surface shallow water equations, non-hydrostatic pressure, dispersive

DOI: 10.3233/ASY-201647

Journal: Asymptotic Analysis, vol. 124, no. 3-4, pp. 343-369, 2021