Stability of Inviscid Parallel Flows between Two Parallel Walls
arXiv:1009.0370
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.
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)