Global modes and transient response of a cold supersonic jet

Global-mode analysis is applied to a cold, M = 2.5 laminar jet. Global modes of the non-parallel jet capture directly both near-field dynamics and far-field acoustics which, in this case, are coupled by Mach wave radiation. In addition to type ( a ) modes corresponding to Kelvin–Helmholtz instability, it is found that the jet also supports upstream-propagating type ( b ) modes which could not be resolved by previous analyses of the parabolized stability equations. The locally neutrally propagating part of a type ( a ) mode consists of the growth and decay of an aerodynamic wavepacket attached to the jet, coupled with a beam of acoustic radiation at a low angle to the jet downstream axis. Type ( b ) modes are shown to be related to the subsonic family of modes predicted by Tam & Hu (1989). Finally, significant transient growth is recovered by superposing damped, but non-normal, global modes, leading to a novel interpretation of jet noise production. The mechanism of optimal transient growth is identified with a propagating aerodynamic wavepacket which emits an acoustic wavepacket to the far field at an axial location consistent with the peaks of the locally neutrally propagating parts of type ( a ) modes.