Sahu, Kirti Chandra; Govindarajan, Rama Stability of flow through a slowly diverging pipe. (English) Zbl 1070.76027 J. Fluid Mech. 531, 325-334 (2005). 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. Cited in 9 Documents MSC: 76E09 Stability and instability of nonparallel flows in hydrodynamic stability Keywords:critical Reynolds number; non-parallel analysis; eigenvalue method PDFBibTeX XMLCite \textit{K. C. Sahu} and \textit{R. Govindarajan}, J. Fluid Mech. 531, 325--334 (2005; Zbl 1070.76027) Full Text: DOI arXiv