**5. Conclusions**

Vortices on sound generation are clearly revealed in edge tones (with thin jets, without any resonators) and cavity tones (with thick, almost semi-infinite, jets, with cavity resonators). Although visible, relatively large vortices are seen in flue instruments driven by thick jets, these are in rare cases. Usually flue instruments are driven by thin jets [(jet length *d*/jet thickness *h*) > 2]. Any visible, discrete vortices do not appear at the flue exit and at the pipe edge in those cases. Instead, vortex layers are formed along the jet upper and lower boundaries, and the acceleration unbalance between them drives the jet as a whole in flue instruments.

The jet-wave drive (or the volume-flow drive) and the vortex-layer drive by thin jets assure sound generation in good manner when the jet enters into the pipe at the instant when the acoustic pressure is maximum. In the discrete-vortex drive by thick jets, the acoustic cross-flow (particle velocity) takes positive and negative values during the passage of the lower and upper vortices from the flue exit to the pipe edge, respectively. These vortex configurations can create sound power during the former and latter halves of an oscillation period.

On the other hand, acoustically induced vortices universally appear as the final dissipation agent. Their role in acoustic energy balance near the saturated state in flue instruments should be reconfirmed in more detail to exactly judge whether the acoustic vortex is generated just at the saturated state or just before the saturated state (at the pre-saturated state).

The receptivity problem is a key point to elucidate the sounding mechanism in flue instruments from the fluid-dynamical viewpoint. The initial amplitudes of acoustic quantities at the flue exit are regarded as the starting point for the acoustic feedback effects upon the jet wave. The vortex-layer model above will then be expected to solve this problem with the aid of direct aeroacoustical simulations.
