# Examining the Quasi-Steady Airflow Assumption in Irregular Vocal Fold Vibration
## 4 Discussion and Conclusions
However, such effects will not appear in the quasi-steady simulations since the flow is steady and there are no interactions between the glottal flow and air inertia in the vocal tract. The two different sets of glottal shapes used in this study provide consistent results, suggesting the glottal shapes have little effect on the validity of the quasi-steady assumption. Compared to those in previous studies, the glottal geometries in the current study are much more complex, including the features of alternating convergent-divergent characteristics, left-right asymmetry, and longitudinal wave propagation, which could occur under irregular vocal fold vibrations. Despite the differences in glottal shape, the errors in the quasi-steady assumption were found to be similar to those reported in previous studies, indicating that glottal geometry has little effect on the validity of the assumption. The quasi-steady and pseudo-static simulations yield very similar results at 100 Hz, indicating that the effect of glottal wall motion is negligible, and deviations from the dynamic simulations are primarily caused by local acceleration (\(\frac{\partial\vec{v}}{\partial t}\)). As mentioned earlier, the importance of glottal wall motion depends on the ratio of wall velocity to flow velocity. At relatively low frequencies, the wall velocity is not significant except at the start and end of the flow cycle, making the unsteady effects of glottal wall motion negligible for most of the cycle. This finding is consistent with previous studies [13; 19], which found that flow unsteadiness due to wall movement is not important. In [PERSON] et al. 's [27] study on respiration, which involved a much lower frequency than phonation, the primary effect of glottal wall motion was on secondary flow in the transverse direction involving flow separation, swirling flows, and vortex shedding. The instability of the main flow in the streamwise direction was mostly influenced by the unsteady acceleration of the flow itself. While this study did not specifically examine phonation, the velocity ratio was similar to that in the current study, suggesting that the conclusion may still be applicable. However, further research is required to confirm this conclusion. In contrast, at high frequencies, such as 500 Hz, glottal wall motion can become important, as evidenced by the differences between the quasi-steady and pseudo-static simulations, particularly during the flow deceleration phase. Furthermore, the momentum budget analysis indicates that the displaced flow due to glottal wall motion may significantly contribute to the convective acceleration. The results of this study suggest that there is no clear relationship between glottal flow unsteadiness and errors of MFDR. In the absence of a vocal tract, increasing vocal fold vibration frequency results in a larger phase shift between quasi-steady and dynamic simulations, but this does not appear to have a significant effect on the skewness of the flow rate waveform and, therefore, on the errors of MFDR. However, when the vocal tract is present, a clear difference in the skewness of the quasi-steady and dynamic flow rate waveforms is observed, resulting in more significant errors of MFDR. Nonetheless, there is still no dependence of MFDR errors on frequency. However, the spectral analysis in this study reveals that at high frequencies, the quasi-steady/pseudo-static prediction of H1-H2 has large errors, indicating that glottal flow unsteadiness still plays a role in determining vocal quality, which is perceptually important. Therefore, although the errors of MFDR do not depend on frequency, glottal flow unsteadiness remains a crucial factor in determining vocal quality at high frequencies. One limitation of this study is that the shape of the supraglottic tract used in the simulation is not realistic. According to [PERSON] et al. [28], the real epilarynx airway is narrower, particularly around the vestibular fold area.