The sounding mechanism of a recorder-like air-jet instrument at low Strouhal number is numerically investigated by three-dimensional direct aeroacoustic simulation and acoustic simulation. Howe's energy corollary is applied to estimate the acoustic energy generation and absorption induced by an oscillating jet and vortex shedding. The quantitative results show that the main acoustic energy generation occurs in the jet downstream, and the absorption occurs in the jet upstream. It is found that the region defined by the Q-criterion identifies the main acoustic energy generation (absorption) region in the downstream (upstream) region of the jet. The results indicate that the vortex shedding mainly induced by the jet deflection gives additional contributions to the acoustic energy absorption. The shed vortices affect the temporal structure of the acoustic energy transfer, in particular, the timing of the double peaks with respect to the jet displacement. If we focus only on the air-jet, the dominant peak is observed when the jet crosses the edge from the inside to the outside of the pipe, as reported in previous experimental works. However, when we include the contributions of shed vortices, the dominant peak appears when the jet dives under the edge, which is consistent with the jet-drive model.

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Dependence of the linear instability to induce a bathtub vortex in a rectangular vessel on the horizontal aspect ratio of the vessel is investigated in the present paper. Water comes in through inlet sections on the top of two facing side walls, and is drained out through a pipe attached to the drain hole at the center on the bottom of the vessel. Water surface is assumed to be always flat without any dip even after instability yielded a large-scale vortex above the drain hole. The flow is steady and symmetric with respect to both vertical center planes along the streamwise direction and perpendicular to it at small Reynolds numbers, but becomes unstable to infinitesimal disturbances inevitably included in the flow at Reynolds numbers larger than a critical value. The steady symmetric flow is numerically obtained, and its stability is analyzed by numerically solving the linear disturbance equation. The instability is confirmed to lead to induction of a so-called bathtub vortex. It is found that there exists a threshold aspect ratio of the rectangular cross section for the instability, and the threshold value is determined.