ON THE STABILITY LOSS OF WEAKLY NONUNIFORM FLOWS IN EXTENDED REGIONS - THE FORMATION OF TRANSVERSE OSCILLATIONS OF A TUBE CONVEYING A FLUID

The stability of weakly non-uniform flows in investigated by the WKB m ethod. Reflecting and refracting wave boundary conditions on the Stoke s lines are considered. Approaches to analysing the situation when the turning points do not lie on the real axis and the eigenfunctions are fairly complex are discussed.As an example, the instability of transv erse oscillations of a weakly inhomogeneous tube conveying a liquid is considered. It is established that under certain conditions a growing oscillatory mode can emerge; it represents a chain of four waves if t he convective instability condition is satisfied, while the local cond ition of absolute instability is not satisfied at any point. A qualita tive analysis of the conditions is carried out in terms of frequencies and wave numbers.