The Linearized 2D Inviscid Shallow Water Equations in a Rectangle: Boundary Conditions and Well-Posedness

TL;DR

This paper analyzes the linearized 2D inviscid shallow water equations in a rectangular domain, proposing boundary conditions that ensure well-posedness and exploring different flow regimes based on reference velocities and height.

Contribution

It introduces boundary conditions that guarantee well-posedness for the linearized 2D inviscid shallow water equations in a rectangle, considering various flow regimes.

Findings

Boundary conditions ensuring well-posedness are identified.

Different flow regimes are characterized based on reference velocities and height.

The analysis covers sub- and super-critical flow cases.

Abstract

We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of boundary conditions is proposed which make these equations well-posed. Several different cases occur depending on the relative values of the reference velocities $(u_0,v_0)$ and reference height $\phi_0$ (sub- or super-critical flow at each part of the boundary).