General stability criterion of two-dimensional inviscid parallel flow

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dc.creatorSun, Liang
dc.date2005-12-22
dc.date2005-12-27
dc.date.accessioned2026-07-07T06:56:19Z
dc.date.available2026-07-07T06:56:19Z
dc.descriptionGeneral stability criterions of two-dimensional inviscid parallel flow are obtained analytically for the first time. First, a criterion for stability is found as $\frac{U''}{U-U_s}>-μ_1$ everywhere in the flow, where $U_s$ is the velocity at inflection point, $μ_1$ 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 $c_r=U_s$ are neutrally stable. Finally, following this principle, a criterion for instability is found as $\frac{U''}{U-U_s}<-μ_1$ 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.
dc.descriptionrevtex4, 4 pages,2 figures
dc.identifierhttps://arxiv.org/abs/physics/0512208
dc.identifierhttp://arxiv.org/abs/physics/0512208
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106592
dc.subjectFluid Dynamics
dc.subjectAstrophysics
dc.subjectAtmospheric and Oceanic Physics
dc.subjectGeophysics
dc.titleGeneral stability criterion of two-dimensional inviscid parallel flow
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