SPECTRAL-ANALYSIS OF PARABOLIZED STABILITY EQUATIONS

In recent years, the parabolized stability equations (PSE) approach ha s gained popularity for transition studies in boundary-layer flows. In this paper, the physical origin df ill-posedness of PSE in the primit ive-variable form is studied by spectral analysis. In subsonic flows, a continuous spectrum representing the upstream-propagating acoustic w aves is shown to be responsible for the ill-posedness of PSE. In super sonic flows, acoustic waves no longer contribute to ill-posedness desp ite the existence of a subsonic region within the boundary layer. In t his case, ill-posedness is caused by some discrete modes with upstream influence. Semi-discretized models of PSE are similarly studied. It i s shown that successful implementation of PSE to physical problems can only be achieved through manipulation of the spectra of the PSE opera tor. A generalized condition for the stable marching solution is devis ed. (C) 1997 Elsevier Science Ltd.