Camassa-Holm Type Equations for Axisymmetric Poiseuille Pipe Flows

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• 作者：Francesco Fedele ; Denys Dutykh
• 关键词：pipe flow ; Poiseuille flow ; Camassa&ndash ; Holm equation ; peakons
• 刊名：Procedia IUTAM
• 出版年：2013
• 出版时间：2013
• 年：2013
• 卷：9
• 期：Complete
• 页码：16-24
• 全文大小：217 K

文摘

We present a study of the nonlinear dynamics of a disturbance to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. The associated Navier-Stokes equations are reduced to a set of coupled generalized Camassa-Holm type equations. These support singular inviscid travelling waves with wedge-type singularities, the so called peakons, which bifurcate from smooth solitary waves as their celerity increase. In physical space they correspond to localized/periodic toroidal vortices or vortexons. The inviscid vortexon is similar to the nonlinear neutral structures found by WALTON (2011) and it may be a precursor to puffs and slugs observed at transition, since most likely it is unstable to non-axisymmetric disturbances.