A uniformly valid asymptotic solution for a transverse jet and its linear stability analysis

An expansion in terms of the ratio λ of the characteristic crossflow velocity U∞ to jet velocity Uj, where λ=U∞/Uj≪1, is used to obtain a representation of the basic three-dimensional steady flow in the nearfield of a transverse jet at large Reynolds numbers and to study its dominant instability. The inviscid vortex sheet analysis of Coelho and Hunt is extended so as to include asymptotic analysis of the viscous shear layers forming along the boundaries of the jet. These not only allow for continuity of the velocity components but also create vorticity whose advection induces an O(λ) axial flow in the direction of the jet. A uniformly valid solution is then constructed for use in a stability analysis that concentrates on the effect of crossflow upon the dominant mode of the free jet. Both the characteristic frequency and growth rate of this mode are found to increase with λ, in qualitative agreement with recent experimental observations.