The acoustic field of sources in shear flow with application to jet noise: convective amplification

Lighthill, in his elegant and classic theory of jet noise, showed that the far-field acoustic pressure of noise generated by turbulence is proportional to the integral over the jet volume of the second time derivative of the Lighthill stress tensor, the integrand being evaluated at a retarded time. The purpose of this paper is to generalize the above results to include the effects of mean flow (velocity and temperature) surrounding the source of sound. It is shown quite generally that the integrand is now a certain functional of the Lighthill stress tensor evaluated at a retarded time. More important, however, at low and high frequencies this functional assumes an extremely simple form, so that the acoustic field can once more be given by integrals of the time derivatives of the Lighthill tensor. Both the self- and the shear-noise contributions to the pressure are evaluated.