## 6 Conclusions  
This work presents a comprehensive investigation of noise reduction on airfoils with regular and irregular leading-edge serrations subjected to turbulent inflow conditions. Through detailed numerical analysis of the mean pressure fields, velocity components, and power spectral density (PSD) of velocity and pressure fluctuations, irregular geometries are found to produce modified spanwise pressure distributions compared to regular serrations, with higher chord spanwise locations contributing to elevated velocity magnitudes. The results demonstrate that irregular leading-edge serrations A3W2 and A6W2 achieve superior noise reduction performance, reaching up to 11 dB in the Strouhal range St = 0.25-0.75. Among regular serration configurations, high-amplitude designs A1W1 and A1W2 achieve up to 10 dB reduction. The A4W2 configuration demonstrate the lowest performance and even shows noise increase between St = 0.6 and 0.8, which may be attributed to its short amplitude characteristics, similar to A2W2, which has been observed to demonstrate inferior noise mitigation performance relative to other variants. This relationship suggests that amplitude length plays an important role in the effectiveness of noise reduction, with shorter amplitudes potentially leading to diminished performance outcomes. Additionally, it is observed that noise reduction tends to exhibit a negative correlation with wavelength parameters. The study reveals that the noise reduction effectiveness of irregular configurations is influenced by the base amplitude of their regular serration counterparts. These findings indicate that irregular serrations possess the capacity to achieve considerable noise reduction. Consequently, it is likely that noise reduction levels could be further enhanced with alternative irregular serration designs.  
Conceptualization, M.N.K., M.M. and W.S.; methodology, M.N.K. and M.M.; validation, M.N.K. and S.S.; investigation, M.N.K.; writing--original draft preparation, M.N.K.;  
Figure 14: PSD of pressure fluctuations for (**a**) regular and (**b**) irregular leading-edge treatments. Sound pressure level differences are provided in the figures (**c**,**d**) (positive values indicate noise reduction).  
writing--review and editing, all authors; visualization, M.N.K.; supervision, M.M. and W.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding. The APC was funded by the Open Acess Publication Fund of RWTH Aachen.  
Not applicable.  
The original contributions presented in the study are included in the article, and further inquiries can be directed to the corresponding author.  
[PERSON] would like to thank TUBITAK (The Scientific and Technological Research Council of Tarkiye) for granting him an International Postdoctoral Research scholarship. [PERSON] gratefully acknowledges Necmettin Erbakan University (Turkiye) for supporting his postdoctoral research stay at RWTH Aachen University. The authors sincerely thank the Gauss Centre for Supercomputing e.V. for providing computing time on the GCS Supercomputer HAWK at Hochstleistungsrechenzentrum Stuttgart.  
The authors declare no conflicts of interest.