2010/09/02 by Hua-Shu Dou, Dou, Hua-Shu
Engineering · Mathematics · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #Chaotic Dynamics (nlin.CD) #Classical Analysis and ODEs (math.CA) #Computational Fluid Dynamics and Aerodynamics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Geophysics (physics.geo-ph) #Navier-Stokes equation solutions #Solar and Stellar Astrophysics (astro-ph.SR) #astro-ph.SR #math.CA #math.DS #nlin.CD #physics.ao-ph #physics.flu-dyn #physics.geo-ph
paper · pdf · doi:10.48550/arxiv.1009.0370
17 pages, 3 figures; Submitted to a journal. In this version, it is explicitly explained why the arbitrary solution of the Euler equations for parallel flows is incorrect physically (see page 10)
openalex publication_date 2010/09/02 · arxiv created 2011/03/06 · arxiv updated 2011/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the stability of inviscid parallel flow between two parallel walls is studied. Firstly, it is obtained that the profile of the base flow for this classical problem is a uniform flow. Secondly, it is shown that the solution of the disturbance equation is cr=U and ci=0, i.e., the propagation speed of the disturbance equals the flow velocity and the disturbance in this flow is neutral. Finally, it is suggested that the classical Rayleigh Theorem on inflectional velocity instability is incorrect which states that the necessary condition for instability of inviscid parallel flow is the existence of an inflection point on the velocity profile.