Modeling and analysis of pooled stepped chutes

TL;DR

This paper models and analyzes pooled stepped chutes using shallow-water equations, providing mathematical conditions for flow coupling, solving a Riemann problem, and presenting numerical experiments relevant to dam spillways.

Contribution

It introduces a mathematical framework for coupled flows in pooled stepped chutes, including conditions for flow interaction and solutions to the Riemann problem.

Findings

Derived coupling conditions for flows between chutes

Provided a well-posedness proof for the coupled system

Conducted numerical experiments demonstrating model behavior

Abstract

We consider an application of pooled stepped chutes where the transport in each pooled step is described by the shallow--water equations. Such systems can be found for example at large dams in order to release overflowing water. We analyze the mathematical conditions coupling the flows between different chutes taken from the engineering literature. We present the solution to a Riemann problem in the large and also a well--posedness result for the coupled problem. We finally report on some numerical experiments.