Compressible Navier-Stokes equations - sound generation and sound radiation

The velocity component v_x (yellow) through the cross section (pink) alongside the resonator. The velocity component v_x is positive, when directed into the resonator and negative when outward. The component contains the particle velocity (germ.: Schallschnelle). One can see the nonlinearities, caused by wind are concentrated in the region of the jet. Deeper inside the pipe only the particle velocity remains. The knot of the particle velocity is located at the closed end of the pipe (left).