Steady nonlinear waves in diverging channel flow

RR Kerswell, OR Tutty, PG Drazin

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)

Abstract

An infinitely diverging channel with a line source of fluid at its vertex is a natural idealization of flow in a finite channel expansion. Motivated by numerical results obtained in an associated geometry (Tutty 1996), we show in this theoretical model that for certain channel semi-angles alpha and Reynolds numbers Re := Q/2nu (Q is the volume flux per unit length and nu the kinematic viscosity) a steady, spatially periodic, two-dimensional wave exists which appears spatially stable and hence plausibly realizable in the physical system. This spatial wave (or limit cycle) is born out of a heteroclinic bifurcation across the subcritical pitchfork arms which originate out of the well known Jeffery-Hamel bifurcation point at alpha = alpha(2)(Re). These waves have been found over the range 5 less than or equal to Re less than or equal to 5000 and, significantly, exist for semi-angles a beyond the point alpha(2) where Jeffery-Hamel theory has been shown to be mute. However, the limit of alpha --> 0 at finite Re is not reached and so these waves have no relevance to plane Poiseuille flow.
Translated title of the contributionSteady nonlinear waves in diverging channel flow
Original languageEnglish
Pages (from-to)231 - 250
JournalJournal of Fluid Mechanics
Volume501
Publication statusPublished - Feb 2004

Bibliographical note

Publisher: Cambridge Univ Press
Other identifier: IDS Number: 809LU

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