Mean flow refraction effects on sound radiated from localized sources in a jet

It is well-known that sound generated by localized sources embedded in a jet undergoes refraction as the acoustic waves propagate through the jet mean flow. For isothermal or hot jets, the effect of refraction causes the deflection of the radiated sound waves away from the jet flow direction. This gives rise to a cone of silence around the jet axis where there is a significant reduction in the radiated sound intensity. In this work, the mean flow refraction problem is investigated through the use of the reciprocity principle. Instead of the direct source Green's function, the adjoint Green's function with the source and observation points interchanged is used to quantify the effect of mean flow on sound radiation. One advantage of the adjoint Green's function is that the Green's functions for all the source locations in the jet radiating to a given direction in the far field can be obtained in a single calculation. This provides great savings in computational effort. Another advantage of the adjoint Green's function is that there is no singularity in the jet flow so that the problem can be solved numerically with axial as well as radial mean flow gradients included in a fairly straightforward manner. Extensive numerical computations have been carried out for realistic jet flow profiles with and without exercising the locally parallel flow approximation. It is concluded that the locally parallel flow approximation is valid as long as the direction of radiation is outside the cone of silence.