Absolute and Global Instability of Plane Submerged Jets

Abstract

The family of velocity profiles of a submerged jet, which are absolutely unstable in the plane-parallel approximation, is considered. The profiles are specified by two parameters: the first of them is responsible for the location of the only inflection point in the velocity profile, and the second is responsible for the shear layer thickness. An algorithm for determining the length of the region of local absolute instability of the jet with a given input velocity profile, that is, the distance at which absolute instability gives way to convective instability, has been implemented. The dependence of this length on the parameters defining the input profile is obtained. A connection between the characteristics of local absolute instability calculated in the plane-parallel approximation and global instability of the jet evolving in space is analytically obtained. The input velocity profile that corresponds to sufficiently large length of the zone of local absolute instability, at which global instability of spatially developing jet occurs, is demonstrated. Thus, the possibility of existence of global instability of plane submerged jets with special velocity distributions is demonstrated.