Author:
Hocking L. M.,Stewartson K.,Stuart J. T.,Brown S. N.
Abstract
An infinitesimal centre disturbance is imposed on a fully Ldveloped plane Poiseuille flow at a Reynolds numberRslightly greater than the critical valueRcfor instability. After a long time,t, the disturbance consists of a modulated wave whose amplitudeAis a slowly varying function of position and time. In an earlier paper (Stewartson & Stuart 1971) the parabolic differential equation satisfied byAfor 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-Rc)t, the amplitudeAdevelops an infinite peak at the wave centre. The possible relevance of this work to the phenomenon of transition is discussed.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference38 articles.
1. Stuart, J. T. 1958 J. Fluid Mech.4,1–22.
2. Stuart, J. T. 1961 Adv. in Aero. Sci.3,121–142.
3. Van Dyke, M. D. 1964 Perturbation Methods in Pluid Mechanics, p.2.Academic Press.
4. Stuart, J. T. 1960 J. Fluid Mech.9,353–370.
5. Benjamin, T. B. 1961 J. Fluid Mech.10,401–419.
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