Extension of the near acoustic field of a jet to the far field

Abstract

The problem of extending the near acoustic field of a high-speed jet to the far field is considered. This is akin to the problem of analytic continuation in complex variable. Analytic continuation is the extension of an analytic function in a limited domain to a larger domain. The general continuation problem involving acoustic sources enclosed by a surface is first analyzed. It is shown that a unique continuation to the far field is possible provided either the pressure or the pressure gradient normal to the surface is given on the surface. In this paper, the continuation is carried out by means of an adjoint Green’s function. One significant advantage of using adjoint Green’s function is that for a given direction of radiation, one is required to solve only a single acoustic scattering problem. Because the present method requires measuring only the fluctuation pressure on the bounding surface whereas other popular methods such as the Kirchhoff integral method or the Ffowcs-Williams and Hawkings equation requires measuring three or more variables, it appears that the present method has definite advantage when it is used to extend an experimentally measured near acoustic field to the far field.