A nonlinear instability burst in plane parallel flow
1972; Cambridge University Press; Volume: 51; Issue: 4 Linguagem: Inglês
10.1017/s0022112072001326
ISSN1469-7645
AutoresL. M. Hocking, K. Stewartson, J. T. Stuart, S. N. Brown,
Tópico(s)Wind and Air Flow Studies
ResumoAn infinitesimal centre disturbance is imposed on a fully Ldveloped plane Poiseuille flow at a Reynolds number R slightly greater than the critical value R c for instability. After a long time, t , the disturbance consists of a modulated wave whose amplitude A is a slowly varying function of position and time. In an earlier paper (Stewartson & Stuart 1971) the parabolic differential equation satisfied by A for two-dimensional disturbances was found; the theory is here extended to three dimensions. Although the coefficients of the equation are coinples, a start is made on elucidating the properties of its solutions by assuming that these coefficients are real. It is then found numerically and confirmed analytically that, for a finite value of ( R-R c ) t , the amplitude A develops an infinite peak at the wave centre. The possible relevance of this work to the phenomenon of transition is discussed.
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