## 3 Aeroacoustic Source Visualization
### Aeroacoustic Sources
This source visualization shows propagating vortical and turbulent structures after the false VFs. From these graphs, we learn that with increasing frequency the characteristic length of the source structures is reduced. Figure 15 shows the convective source term, the local time derivative of the pressure and the sum of those. Therefore, the corresponding values at the centerline in the x-direction are evaluated at the four characteristic time steps that were used in the previous discussion. To calculate the convective source term on the centerline, the pressure gradient was approximated by the local derivative in x-direction \(\frac{\partial p}{\partial x}\), which is valid, because the y- and z-components of the mean velocity \(\overline{\mathbf{u}}\) are negligible inside the center yz-plane of the whole computational domain. Based on Figure 15, we can explain the results of the previous source term analysis in [43]. First of all, the convective source part \(\overline{\mathbf{u}}\cdot\
abla p\) is localized inside the glottis gap and is of about one magnitude larger than the time derivative source part \(\frac{\partial p}{\partial t}\). However, the time derivative has a larger spatial extend and the integral contribution is larger (discussed later in Figure 16). This global sum over the source terms gives an expectation of the relevancy in the resulting voice sound spectra in the far field. This let us conclude that the convective part is probably not so relevant. From the time instances in Figure 15, we learn that if the gap is narrow, the gradient term is larger, and dominates the visualization (as featured in [43]). If the gap widens, the peak of the convective term is reduced significantly. For a fully open glottis gap, the convective part and the time derivative part have a similar magnitude. This let us conclude that in the case of glottis insufficiency, we see that the convective term is decreases with increasing insufficiency [43]. Mostly, this was found to be a reduction of the pressure gradient with increasing insufficiency [49]. Having extensively investigated the spatial distribution of the acoustic source term in the time and frequency domain, the source terms are now also investigated globally, to get an idea of the energy content related to certain frequencies. For doing so, the absolute value of the Fourier transformed, conservatively interpolated acoustic source term (RHS  
Figure 16: Normalized sum of the absolute values of the finite element sound sources of the partial time derivative of the incompressible pressure and the convective source term. The values, plotted on the \(y\)-axis, are normalized by the maximum value of the data. Figure 15: Comparison of the pressure time derivative and convective source term along the center line in x direction (see Figure 2). of Equation (6)) is summed over all nodes inside the source region. The resulting spectra of the two source term contributions of the PCWE are depicted in Figure 16. Therein, the non-harmonic contribution to the source term is depicted by simple thin lines, whereas the harmonics of the VF vibration are indicated by dots. The spectrum essentially represent the energy content of the primary voice signal, which is the arising sound before it is modified by the filter characteristics of the vocal tract. The result shows that the convective term has a noteworthy contribution to the total source term in the low frequency range up to about 800 Hz (5\(f_{0}\)). In general, the tonal components dominate the spectrum in the lower and middle frequency range, whereas in the higher frequency range the broadband contribution increases and has considerable amplitudes. Regarding a prospective propagation simulation, we can conclude that the convective term might have an impact on the resulting acoustic spectrum in the lower frequency range. Figure 17 shows the total PCWE source term during a full cycle. Again, we see the four phases. Firstly, the developing glottal jet during opening VFs. Secondly, a fully developed glottal jet at maximum strength.