## 2 Mechanism of Low-Frequency Pressure Fluctuation
### Resonance Mechanism of Low-Frequency Pressure Fluctuation
#### 2.2.2 Planar Standing Wave in Plenum
The large-scale vortices on both sides of the jet can exhibit either symmetric or antisymmetric patterns. [PERSON] et al. [22] noted that the resonance between the standing wave and edgetone feedback strengthens the antisymmetric vortex mode. As a result, the antisymmetric vortex mode dominates the edgetone feedback and serves as an energy source for the width-direction standing wave, as illustrated in Figure 3.  
Figure 2: Schematic of the pressure standing wave in the plenum of LAWT, as viewed from the collector towards the nozzle. Note that \(y_{M1}\) corresponds to the negative value of \(y_{M2}\). Originally shown in [22]. Due to the antisymmetric characteristics of the standing wave, its amplitude approaches zero at the center of the jet and increases as it moves away from the center (as depicted in Figure 2). Hence, the pressure standing wave is more prone to interact with the external feedback loop of edgetone feedback. Consequently, when resonance between the edgetone feedback and the standing wave occurs, its frequency aligns closer to that of the external feedback loop rather than internal feedback [22]. * Planar standing wave in SKLA-01  
After discovering widthwise planar standing waves as a resonant excitation source for LAWT wind tunnels, [PERSON] et al. built a 1:20-scale LAWT wind tunnel (SKLA-01) with a width-adjustable plenum.Their results revealed the presence of planar pressure standing waves in all three directions of the plenum; however, these standing waves were comparatively weaker in the other two directions compared to the width direction [25; 49]. The analysis by [PERSON] et al. [25; 49] showed that the standing wave frequency in the vertical direction of the plenum is close to that of a circuit standing wave mode in the wind tunnel. Since there was no direct energy injection into these two standing wave modes, [PERSON] et al. [25; 49] speculated that these two modes appeared because they satisfied the resonance condition, which led to self-excited oscillations through the resonance mechanism between them by capturing energy from the airflow. [PERSON] et al. [25; 49] did not provide any information about the excitation source for the longitudinal standing wave of the plenum. Considering that the length (\(L_{x}\)) and width (\(L_{y}\)) of the plenum were quite close (\(L_{x}/L_{y}=1.04\)), so that the longitudinal standing wave mode also satisfied the resonance condition with the edgetone, the authors of this paper speculate that the longitudinal standing wave may also have developed in the process of resonance with the edgetone feedback. The reason why the pulsation intensity of the longitudinal standing wave was lower than that of the transverse standing wave may be due to the lack of antisymmetric modes in the shear layer as an energy transfer intermediary for the longitudinal standing wave. [PERSON] et al. [25; 49] found that the addition of a floor to the plenum of the SKLA-01 wind tunnel (as shown in Figure 4) significantly enhanced the widthwise standing wave mode. The underlying cause of this phenomenon remains unclear, and [PERSON] et al. [49] hypothesized that it may be because the pressure above the floor is lower than that below during wind tunnel operation, resulting in the formation of vortex pairs similar to wingtip vortices on either side of the floor. The relative strengths of these two vortices alternated under the influence of the anti-symmetrically distributed standing wave, which in turn enhanced the widthwise pressure standing wave. Figure 3: Schematic of the interaction of the transverse standing wave with the antisymmetric vortex mode. Originally shown in [22]. * Other cases of resonance between plenum standing wave and edgetone Although it has not been reported until recently [22], the probability of resonance between the planar standing wave modes in the three directions of the plenum and the edgetone feedback is quite high.