## 3 Aeroacoustic Source Visualization
### Aeroacoustic Sources  
This section deals with the shape and location of the aeroacoustic sources. We examine the sources in the time and frequency domain and expect to receive significant insight into important flow characteristics. Figure 11 shows the convective part of the PCWE source term and contour lines for four time instances. In general, we can interpret this source term as a projection of the pressure gradient onto the mean velocity (some sort of flow blending). Therefore, we will see large contributions in areas where the flow velocity is large (consequently between the VFs and inside the area of the glottal jet). In the case of opening vocal folds, the source term contours indicate that flow accelerates a plume into the vocal tract looking like a mushroom. This process continues until the VFs are fully open. In the case of fully open VFs, the source iso-contours indicate well developed fluctuations inside the glottal jet. From this time instance on, the VFs are closing. During constriction of the glottal gap, the velocity and the pressure contours still propagate into the vocal tract and widen the contours of the source term. Finally, in the case of fully closed VFs, the driving energy is at minimum. The flow is resting, the previously developed vortices are decaying, and the sources are reduced drastically. Figure 12 shows convective part of the source term at two frequencies in a time-harmonic visualization of the oscillation mode. It again shows the main area of influence of the convective part inside the glottal jet region, as well as the decrease in size of the source structures with increasing frequency for both high harmonic and non-harmonic frequencies. Figure 13 visualizes the partial time derivative of the pressure for four time instances. Firstly, the illustrations show similar trends as the mean pressure convection plots. During opening, structures are formed and convect downstream. When the VFs are fully open, the sources show vortical structures that are connected to a stable jet. During closing, the jet energy is reduced which causes a negative pressure envelope. Furthermore, the flow resistance between the VFs increases rapidly and lowers the pressure level towards zero inside the sub-glottal region during closing. This increasing flow resistance causes negative source structures for the closed VFs. From this analysis, we can learn two important general facts: Firstly, if the VFs are not fully closing the source energy (at specific time instances) VFs motion does not provide as much source energy to the flow-induced sound sources as in the case of a healthy voice. Secondly, if the VFs are not fully closing the source energy during one cycle is not cut off entirely and therefore turbulent and vortical structures are  
Figure 10: Pressure gradient visualization for two frequencies. permanently present. These turbulent structures increase the broadband component of the voice signal. The findings highlight the importance of glottal closure for a high voice quality and supports the research output of several studies reporting smaller harmonic amplitudes of a voice affected by glottal insufficiency [49; 50]. Figure 14 shows the spatial distribution of the time derivative of incompressible pressure in the frequency domain at two characteristic frequencies. Based on the Fourier transformation, the shapes are tightly connected to the pressure distribution of Figure 5. The visualization at the VF driving frequency shows that source contours dominate the whole visualization domain. The spatial distribution of the first time derivative of the incompressible pressure is similar to the shape of the incompressible flow pressure at this frequency. Thus, the first term reaches far into the sub-glottal region (see Figure 6). At frequency (\(f=3589\,\mathrm{Hz}\)), we see that the incompressible pressure distribution and the time derivative are nearly equivalent since the Fourier transformation features a prefactor of \(-i\omega\).