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The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and that have been previously detected as tones in the near-nozzle region. Using three models (the linearized Euler equations, a cylindrical vortex sheet, and a cylindrical duct with pressure release boundary conditions), we show that these waves can be described by linear modes of the jet and correspond to acoustic waves that are trapped within the potential core. At certain frequencies, these trapped waves resonate due to repeated reflection between end conditions provided by the nozzle and the streamwise contraction of the potential core. Our models accurately capture numerous aspects the potential core waves that are extracted from large-eddy-simulation data of a Mach 0.9 isothermal jet. Furthermore, the vortex sheet model indicates that this behavior is possible for only a limited range of Mach numbers that is consistent with previous experimental observations.

Trapped acoustic waves in the potential core of subsonic jets