Including acoustic modes in the vortex-sheet eigenbasis of a jet

Vortex-sheet (V-S) models of jets are widely used to describe the dynamics of modes, such as the Kelvin-Helmholtz instability and guided acoustic waves. However, the absence of the free-stream acoustic modes in the V-S eigenspectrum is seldom pointed out in the literature. This family of modes is important if, for example, one is interested into the problems of sound emission or flow-acoustic interactions. In this work, it is shown how a distantly confined jet may be used as a surrogate problem for the free jet, in which the free-stream acoustic waves appear as a set of discrete modes. Comparing the modes observed in the free jet with those of the distantly confined jet, we show that other than the free-stream acoustic modes, the eigenvectors and eigenvalues converge exponentially with the wall distance. The proposed surrogate problem, thus, efficiently reproduces the dynamics of the original problem while accounting for the dynamics of the free-stream acoustic eigenmodes.