Note on the stability of plane parallel flows

Extract

The subject of this note is the behaviour of three-dimensional small disturbances to plane parallel flows, which have a variation in the direction normal to the plane of mean flow, in relation to two-dimensional disturbances which vary in the plane of mean flow only. It was pointed out by Squire (1933) that, in linearized theory, the disturbancewhichisneutrallystable at the criticalReynolds number R, is two-dimensional in form. More recently interest has turned to the question as to which kind of disturbance is most rapidly amplified at a given Reynolds number above the critical. Jungclaus (1957) pointed out that for certain values of R and of the resolved wavelength in the plane of mean flow, three-dimensional disturbances may be more unstable than plane ones. Recently, Watson (1960) has shown further that a two-dimensional disturbance is the one most rapidly amplified in a certain range of R starting from the critical. In thi8 note we take a slightly different view of the problem which enables us to define specifically the upper end of this range of R, when it exists.