On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flow

摘要: This paper considers the nature of a non-linear, two-dimensional solution Navier-Stokes equations when rate amplification disturbance, at given wave-number and Reynolds number, is sufficiently small. Two types problem arise: (i) to follow growth an unstable, infinitesimal disturbance (supercritical problem), possibly state stable equilibrium; (ii) for values number which no unstable exists, decay finite from possible equilibrium down zero amplitude (subcritical problem). In case existence implies disturbances. Numerical calculations, are not yet completed, required determine two behaviours arises in plane Poiseuille flow, range number.It suggested that method this (and generalization described by Part 2 J. Watson) valid wide numbers wave-numbers inside outside curve neutral stability.