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Stability of flow through a slowly diverging pipe. (English) Zbl 1070.76027

Summary: 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 is obtained at the threshold of inviscid stability. A non-parallel analysis yields linear instability at surprisingly low Reynolds numbers, of about 150 for a divergence of \(3^\circ\), 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.

MSC:

76E09 Stability and instability of nonparallel flows in hydrodynamic stability
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