Abstract
Formation of the secondary self-oscillating modes of flow branching away from the Poiseuille flow in a plane channel, is investigated. Conditions of appearance of the secondary self-oscillating modes at nearly critical values of the Reynolds number were obtained earlier in [1, 2]. It was shown, in particular, that the existence of the secondary flows can be established by analyzing the linearized equations only. In the present paper the formation of secondary flows in a plane channel, periodic in x and t, is studied with help of the asymptotic solutions of the Orr — Sommerfeld equations. It is proved that in the sufficiently small neighborhood of almost every value of the Reynolds number R lying on the neutral curve of the linear theory of stability, values of R exist such that the Navier — Stokes equations have solutions periodic in x and t.
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