# Numerical Investigation of Tonal Trailing-Edge Noise Radiated by Low Reynolds Number Airfoils
## 5 Discussion of Results
This allows for an important modification to the AFL scenario originally proposed by [PERSON] (2018), as illustrated in Figure 29. The additionally required condition is the ability of the vorticity modes to sustain their presence and sufficient amplitude to the TE for the effective acoustic scattering process to take place. Hence, the LSB must be located close enough to the airfoil TE to prevent the subsequent destruction of the saturated coherent modes (rollers) through turbulent BL transition and spanwise mixing process. Finally, the AFL frequency selection mechanism was addressed. It was noted that, for a low \(Re_{c}\) laminar flow around a symmetric NACA-0012 airfoil, [PERSON] and [PERSON] (2019) identified the shedding frequency with that of the most amplified near-wake K-H instability in the free shear layer. The TE scattering of such near-wake instability was claimed as the source of the shedding tone in the absence of AFL. It is plausible that such a wake instability mechanism may superimpose on the AFL mechanism of airfoil tonal noise production,  
Figure 29: Suggested acoustic feedback loop (revised from [PERSON] (2018)). with both related to the TE scattering of the nonlinearly saturated K-H modes. This points to the mutual resonant interaction wherein both mechanisms overlap and appear to enhance each other. To this end, when the airfoil flow is laminar with no AFL present, the remaining shedding tone appears at a significantly lower amplitude, as demonstrated by [PERSON] and [PERSON] [9]. On the other hand, when the AFL mechanism is suppressed due to BL tripping or a low-intensity upstream turbulence, the observed acoustic spectrum still reveals a broadband hump centered around the shedding frequency. It thus appears that the naturally primary shedding mechanism is dominant and amplified by the AFL presence due to the mutual interference and resonant interaction of the AFL-selected frequencies with the shedding tone. The latter essentially elevates that part of the spectrum of the amplified BL instability modes that appears the closest to the shedding tone. This may explain the divergence between the frequencies of the most amplified instability modes and the acoustically radiated peak tone coinciding with the shedding frequency. It is the interaction of the two mechanisms that produce the dual ladder-type acoustic tonal structure of [PERSON] et al. [1], with multiple AFL-selected tones staged around the shedding tone. Formal analysis, L.N. and V.G. ; Investigation, L.N. and G.Y. ; Supervision, V.G., M.R. and R.M. ; Validation, L.N. and G.Y. ; Writing--original draft, L.N. ; Writing--review and editing, V.G. All authors have read and agreed to the published version of the manuscript. This research was partially funded by the Air Force Office of Scientific Research (Program Manager Dr. [PERSON]), grant number FA9550-12-1-0126. Not applicable. All data presented in this study is original. Partial support for this work through Florida Center for Advanced Aero Propulsion is acknowledged. Very helpful discussions with [PERSON] (AFRL) are highly appreciated. The authors declare no conflict of interest.