Abstract
Many studies, both theoretical and experimental, have been dedicated to the stability of flow in a circular tube (see, for example, review [1]). In every case mathematical investigation has not succeeded in obtaining an expression for hydrodynamic instability of such a flow for disturbances of sufficiently low amplitude. (An exception is [2].) Experiment also indicates the stability of such a flow [3], with a laminar mode being extended to Reynolds numbers of the order of tens of thousands. These facts are the basis for the assumption that the flow of a viscous incompressible liquid in a circular tube is stable for small perturbations. However, there is no analytical or even numerical proof of this hypothesis. Moreover, some studies, for example [2], indicate the instability of such a flow in relation to three-dimensional nonaxiosymmetric perturbations. The analysis of hydrodynamic stability with respect to three-dimensional disturbances of flow within a circular tube conducted in this study showed the stability of the flow over a wide range of wave numbers and Reynolds numbers.
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A. Davey and P. G. Drazin, “The stability of Poiseuille flow in a pipe,” J. Fluid Mech.,36, pt. 2 (1969).
W. P. Graebel, “The stability of pipe flow, pt. 1. Asymptotic analysis for small wave numbers,” J. Fluid Mech.,43, pt. 2 (1970).
R. J. Leite, “An experimental investigation of the stability of Poiseuille flow,” J. Fluid Mech.,5, No. 1 (1959).
M. A. Gol'dshtik and V. A. Sapozhnikov, “Stability of flow in a toroid channel,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 4 (1971).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 20–24, January–February, 1973.
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Vil'gel'mi, T.A., Gol'dshtik, M.A. & Sapozhnikov, V.A. Stability of a flow in a circular tube. Fluid Dyn 8, 16–19 (1973). https://doi.org/10.1007/BF01017630
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DOI: https://doi.org/10.1007/BF01017630