Near field jet noise by acoustic wave radiation

We consider the problem of noise emission in supersonic jets by radiation of acoustic waves into the far field. The initial part of the jet close to the nozzle with a constant core flow is examined, which contributes significantly to noise emission. The plane parallel jet is modelled as a composition of two opposite parallel hyperbolic tangent shear flows allowing us to derive exact solutions as expansions about singularities for the underlying linearized Euler equations for compressible fluids. Using this we analyze two effects of acoustic wave radiation into the far field: (i) we derive acoustic waves directly radiated by the shear layers which seem to be linked to a class of unstable jet modes described by Tam & Hu (1989); (ii) the opposition arrangement of the shear layer leads to an interaction of the wave phenomena. Waves are both partially reflected, leading to trapped waves, and partially transmitted to the outside of the jet, thus contributing to radiation. For both radiation effects, we study the influence of Mach number on characteristic quantities of the radiated waves, such as propagation angle. The key observations were confirmed by DNS with the analytical eigenfunctions used as initial DNS values.