On small disturbances of plane couette flow

Abstract

The Orr-Sommerfeld equation for the function q,(y) , which appears in the component q,(y)explia(x-ct) I of the stream function, is analyzed in detail for the case of plane Couette flow . A set of solutions is found whose asymptotic behavior as aR--> '" can be calculated in the whole complex v-plane (R is the Reynolds number) . A disturbance with given a is proved stable, for any a, if aR is s uffi~iently lar~e. In ad9itio~, an inves.ti&ati~n is made of the asymptotic properties of an alhed equatIOn for WhICh, Jt1 contradlstll1ctlOll to the singular Couette case. an inner friction layer does exist.