Virginia TechRenardy, Michael J.2014-05-282014-05-282008Renardy, M., "Short wave stability for inviscid shear flow," SIAM J. Appl. Math., 69(3), 763-768, (2008). DOI: 10.1137/0807209050036-1399http://hdl.handle.net/10919/48133We consider the linear stability of inviscid shear flows. While it is well known that discontinuous velocity profiles lead to short wave instabilities and ill-posedness, known examples of instability for smooth profiles have a short wave cutoff; i.e., there is a critical wave number beyond which no unstable eigenvalues exist. This paper proves a result to this effect under suitable assumptions on the base flow profile.application/pdfenIn Copyrighthydrodynamic stabilityrayleigh equationinviscid shear flowmathematics, appliedArticle - Refereedhttp://epubs.siam.org/doi/abs/10.1137/080720905https://doi.org/10.1137/080720905