Camassa-Holm type equations for axisymmetric Poiseuille pipe flows
Abstract
We present a study on 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 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.
Keywords
Cite
@article{arxiv.1211.4233,
title = {Camassa-Holm type equations for axisymmetric Poiseuille pipe flows},
author = {Francesco Fedele and Denys Dutykh},
journal= {arXiv preprint arXiv:1211.4233},
year = {2019}
}
Comments
11 pages, 4 figures, 31 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/