Roll-waves in bi-layer flows

TL;DR

This paper derives shallow water equations for bi-layer Newtonian fluid flows down a ramp, analyzes their stability, and identifies conditions under which roll-waves, a type of hydrodynamic instability, occur.

Contribution

It provides a new derivation of consistent shallow water equations for bi-layer flows and analyzes the spectral stability, revealing conditions for roll-wave formation.

Findings

Identification of hydrodynamic instabilities in bi-layer flows

Spectral analysis of steady flow stability

Conditions leading to roll-wave occurrence

Abstract

In this paper, we derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of hydrodynamic instabilities, so called roll-waves, when steady flows are unstable.