The linear stability of plane Poiseuille flow under unsteady distortion

The application of multi-scale perturbation method to the stability analysis of plane couette flow

“…The basic laminar flow isU=y, sold w --0, and the threshold amplitude is the same whether 6>0 or o']'~0, The multi-scale analysis can predict only the instability under one sign of ~, and in the plane Couette flow, we lost the result consistence between these two methods as seen is Ref. [3], J~ is quite different from ~1' 1 and Jt especially in Example 2.…”

“…[3] to the analysis of plane Couette flow and compare tile numerical results with those in plane Poiseuille flow. it is shown that the multi-scale analysis is effective to the problem of linear stability of distorted laminar flow, but under some restriction, to the problem of bifurcation from infinity.…”

“…[3]. the frequency anc't the threshold of neutral T-S wave are respectively: (I) a=l.29 R =2900, ~/r/R =14.066 By the method of Ref.…”

“…[3]. Ihe dc,,eloprnenl Of disturbances with time has ah'eadv been classified as the h~llox~ing po.,,si hllilics: (I) c~2>0, tile distrub~,nce ~ill grox~ at last ~ hatexer ~s, be.…”

“…[I] by physical assumption, then suggested in Ref. [3] a multi-scale perturbation method to solve the partial differen.tial equations with the time factor e -vj . When this multi-scale method is used to investigate the stability of plane Poiseuille flow, some reasonable results conformable to those obtained in Ref.…”