Roll-waves in bi-layer flows

2011/02/23 by Marc Boutounet, Boutounet, Marc, Pascal Noble +4
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.1104.5154

arxiv created 2011/02/23 · openalex publication_date 2011/02/23 · arxiv updated 2011/04/28 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

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.

Related

• Note on the stability of viscous roll-waves
• Formation and evolution of roll waves in a shallow free surface flow of\n a power-law fluid down an inclined plane
• Whitham's equations for modulated roll-waves in shallow flows
• The Stability of Roll-Waves in Two-Phase Pipe Flow
• Multidimensional stability and transverse bifurcation of hydraulic shocks and roll waves in open channel flow