Stability of flow through a slowly diverging pipe

Details Stability of flow through a slowly diverging pipe Stability of flow through a slowly diverging pipe

2004-09-07

arxiv.org/abs/physics/0409037v2

Physics

Fluid Dynamics

9 pages, 15 figures, accepted to J. Fluid Mech

Scientific paper

10.1017/S002211200500399X

Although the critical Reynolds number for linear instability of the laminar flow in a straight pipe is infinite, we show that it is finite for a divergent pipe, and approaches infinity as the inverse of the divergence angle. The velocity profile at the threshold of inviscid stability is obtained. A non-parallel analysis yields linear instability at surprisingly low Reynolds numbers, of about 150 for a divergence of 3 degrees, which would suggest a role for such instabilities in the transition to turbulence. A multigrid Poisson equation solver is employed for the basic flow, and an extended eigenvalue method for the partial differential equations describing the stability.

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