General stability criterion of two-dimensional inviscid parallel flow

الأصل · EN

General stability criterions of two-dimensional inviscid parallel flow are obtained analytically for the first time. First, a criterion for stability is found as U''/U-Uₛ>-μ₁ everywhere in the flow, where Uₛ is the velocity at inflection point, μ₁ is eigenvalue of Poincaré's problem. Second, we also prove a principle that the flow is stable, if and only if all the disturbances with cᵣ=Uₛ are neutrally stable. Finally, following this principle, a criterion for instability is found as U''/U-Uₛ<-μ₁ everywhere in the flow. These results extend the former theorems obtained by Rayleigh, Tollmien and Fjørtoft and will lead future works to investigate the mechanism of hydrodynamic instability.