The paper presents experimental investigations of the low-density air-helium jets. The paper is aimed at the analysis of the flow conditions promoting the local absolute instability leading to global flow oscillations. A number of the test cases are analysed with a wide range of the shear layer thickness showing conditions favorable for the global modes and also mixing intensity triggered by such a regime. It is shown that high mixing intensity is determined not only by the global regime but also by the vortex pairing process. The results are compared with a recently proposed universal scaling law for an onset into the global mode. The results turn out to be far from this scaling law and the reasons for such discrepancies are discussed. The measurements show also that if the shear layer at the nozzle exit is thin enough the global modes are suppressed. The mechanism leading to the global mode suppression under such conditions is carefully analysed.