Stability of Inviscid Parallel Flows between Two Parallel Walls
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2010
 arXiv:
 arXiv:1009.0370
 Bibcode:
 2010arXiv1009.0370D
 Keywords:

 Physics  Fluid Dynamics;
 Astrophysics  Solar and Stellar Astrophysics;
 Mathematics  Classical Analysis and ODEs;
 Mathematics  Dynamical Systems;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Atmospheric and Oceanic Physics;
 Physics  Geophysics
 EPrint:
 17 pages, 3 figures