**Author details**

displacement model. Their simulation results (see Figures 7, 9, and 10 and Table IV in [56]) seem to confirm the non-zero amplitude at the flue exit, and the acoustic

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

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

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

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.

The present author expresses his appreciation to three European scientists: Dr. Judit Angster of Fraunhofer-Institute fur Bauphysik, in Stuttgart, for her long-term support to carry out the PIV measurement; Prof. Avraham Hirschberg of Technishe Universiteit Eindhoven for his kind offer of the picture used as **Figure 12(c)** and helpful comments to the author's journal papers from the aeroacoustical viewpoint; and Prof. Andreas Bamberger of Freiburg University for his effective comments and suggestions on the PIV. Also, the author thanks Keita Arimoto and Takayasu Ebihara of Yamaha Corporation, in Hamamatsu, Japan, for their sincere support

feedback effects on the jet wave may be given at its starting point.

unbalance between them drives the jet as a whole in flue instruments.

the former and latter halves of an oscillation period.

and appropriate comments to the manuscript.

state (at the pre-saturated state).

**Acknowledgements**

**74**

**5. Conclusions**

*Vortex Dynamics Theories and Applications*

Shigeru Yoshikawa Kyushu University, Dazaifu, Japan

\*Address all correspondence to: shig@lib.bbiq.jp

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
