Exact solution describing a shallow water flow in an extending stripe

TL;DR

This paper presents an exact partially invariant solution to the (2+1)D shallow water equations that models fluid flow in an extending stripe with sources and drains, including smooth flow and hydraulic jumps.

Contribution

It introduces a novel exact solution for shallow water flow in an extending stripe, incorporating linear sources and drains, and analyzes flow behaviors such as hydraulic jumps.

Findings

Solution describes smooth flow and hydraulic jump phenomena.

Particle trajectories and sonic characteristics are calculated.

Flow extension modeled by linear source and drain boundaries.

Abstract

Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump are possible. Particle trajectories and sonic characteristics on the obtained solution are calculated.