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

Vortex-sheet models of jets are widely used to describe the dynamics of modes, such as the Kelvin-Helmholtz instability and guided acoustic waves. However, it is seldom pointed out in the literature the absence of the free-stream acoustic modes in the vortex-sheet spectrum. This indicates that free-stream sound waves are not eigensolutions of the parallel jet. This family of modes is important if, for example, one is interested in problems of sound emission or flow-acoustic interactions. In this work we show how a distantly-confined jet may be used as a surrogate problem for the free jet, in which 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 with wall distance. The proposed surrogate problem thus efficiently reproduces the dynamics of the original problem, while allowing to account for the dynamics of free-stream acoustic modes.