## 3 Aeroacoustic Source Visualization
### Flow Quantities  
Before we start with the visualization of the aeroacoustic source terms, we visualize the flow field. In particular, the flow pressure distribution, the turbulent kinetic energy (TKE), the velocity field, the mean velocity, and the gradient of the flow pressure are investigated systematically. Figure 4 shows the flow pressure distribution and contour surfaces for four time instances. The contour values have been selected to provide an illustrative visualization of the physical quantity inside the supra-glottal area. In the case of opening vocal folds, the high value of the pressure and the flow pressure contours indicate that flow is accelerated and turbulent structures are blown out of the region between the false VFs. The highly developed turbulent structures are caused by a local flow pressure decrease after the VFs (indicating a developing glottal jet) when the VFs are opening. This process continues until the VFs are fully open. In the case of fully open VFs, the flow pressure iso-contours indicate a compact glottal jet. Due to the high jet velocity the dominating pressure contour is negative. From this time instance on, the VFs are closing and constrict the glottal gap. This constriction reduces and diffuses the velocity jet and the flow pressure starts to rise in the supra-glottal area. In the case of fully closed VFs, the flow pressure is positive again with spatial fluctuations due to the decaying vortices that are localized in a resting fluid. The flow is cut off, the driving force of the fluid jet is close to zero, and the flow intensifies curling. Having obtained the finely resolved source term, a field fast Fourier transformation (field FFT) is performed in \(MATLAB^{\copyright\). The field FFT is an FFT of the time signal, performed for every nodal value on the computational grid. For the following plots, the oscillation mode of the Fourier transformed nodal values is chosen to be visualized time-harmonically employing iso-surfaces [48]. Figure 5 shows the pressure distribution for two characteristic frequencies. The visualization at the VF fundamental frequency shows that pressure contours dominate the whole domain. The contour visualizes a gradual pressure drop in x direction. The spatial distribution of the pressure at this frequency is equivalent to the shape of the first time derivative of the pressure. Therefore, the first term of the PCWE source term will reach far into the sub-glottal region. This fact will be further investigated by Figure 6 and the  
Figure 3: GAW during one full cycle with indicated, investigated, four time steps, which are marked by the vertical bars. next paragraph. In contrast to the fundamental frequencies and the higher multiples of it, we investigate the pressure distribution at a different frequency. This visualization has the shape of propagating vortical structures, depicted as differently colored conglomerates indicating a phase shift. In this paragraph, we provide evidence for the dominant spatial distribution of first term in the PCWE source. Figure 6 shows the flow pressure and velocity within the domain along the center line in x-direction at the above introduced phases of VF oscillation. We have to note that the pressure values at initial and final position are constant as a consequence of the flow boundary condition. In general, the pressure distribution is segmented into four areas along a streamline. Firstly, the pressure increases partly due to the approaching high flow resistance. Secondly, within the glottis gap the pressure drops significantly and the flow is accelerated. Thirdly, downstream the glottis gap, vortical and  
Figure 4: Fluid pressure vizualization during a full VF cycle. Figure 5: Fluid pressure vizualization for two frequencies. Figure 6: Fluid pressure and velocity over the computational domain. turbulent structures cause pressure and velocity fluctuations. Finally, the pressure and the velocity fluctuations decay towards the flow boundary.