Can we describe acoustic eigenmodes with a vortex sheet in a jet?

Vortex sheet is widely used as a simplified model for a variety of shear flows, e.g. jets and wakes, to describe the dynamics of modes, such as the Kelvin-Helmholtz mode or guided acoustic waves. Nevertheless, it has never been pointed out in the literature the absence of free-stream acoustic modes in the vortex-sheet eigenspectrum. These modes are important when describing noise emissions or flow-acoustic interaction phenomena. We here show that the unconfined vortex-sheet model, usually adopted to solve the free-jet eigenvalue problem, does not include free-stream acoustic modes and we propose the use of a distantly-confined vortex-sheet model as a surrogate problem for the free jet in which the missing acoustic branch appears together with all of the other discrete jet modes of the original free-jet problem.