Compressible Navier-Stokes equations - Sound generation and sound radiation

Turbulent kinetic energy k (red) inside an organ pipe, sampled through the lower one-third (pink) of the cross section alongside the resonator. Large values of k mean high friction. The black line is k, integrated in time. The small, high peak (left) is caused by the boundary layer at pipes bottom. The time-average shows that the irregular behavior of k forms a distribution, which slopes down exponentially. The position of the distribution marks the position of the rotating primary (and secondary) vortex in the bottom of the organ pipes resonator. Here the wind field couples on the acoustic field.