Abstract
A linearized problem of stability with respect to a three-dimensional pattern of perturbations in a steady flow of a viscous Newtonian fluid in a tube (the Poiseuille flow) is analyzed. The time evolution of individual harmonics of perturbations in angular and axial directions is studied. The transition to quadratic functionals constructed on the squares of the moduli of perturbation velocity components and their radius derivatives is performed. An upper estimate is obtained for the stability parameter and is used to derive lower estimates for the critical Reynolds numbers in the cases of axisymmetric perturbations as well as in the cases of two-dimensional axisymmetric and nonaxisymmetric rz perturbations.
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