Steady nonlinear waves in diverging channel flow

Kerswell, R.R., Tutty, O.R. and Drazin, P.G. (2004) Steady nonlinear waves in diverging channel flow. Journal of Fluid Mechanics, 501, 231-250. (doi:10.1017/S0022112003007572).

Record type: Article

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 ? and Reynolds numbers Re := Q/2? (Q is the volume flux per unit length and ? 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 ? =?2(Re). These waves have been found over the range 5 ? Re ? 5000 and, significantly, exist for semi-angles ? beyond the point ?2 where Jeffery–Hamel theory has been shown to be mute. However, the limit of ??0 at finite Re is not reached and so these waves have no relevance to plane Poiseuille flow.

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