  An integral formulation for acoustic radiation in moving flows is presented.
It is based on a potential formulation for acoustic radiation on weakly
non-uniform subsonic mean flows. This work is motivated by the absence of
suitable kernels for wave propagation on non-uniform flow. The integral
solution is formulated using a Green's function obtained by combining the
Taylor and Lorentz transformations. Although most conventional approaches based
on either transform solve the Helmholtz problem in a transformed domain, the
current Green's function and associated integral equation are derived in the
physical space. A dimensional error analysis is developed to identify the
limitations of the current formulation. Numerical applications are performed to
assess the accuracy of the integral solution. It is tested as a means of
extrapolating a numerical solution available on the outer boundary of a domain
to the far field, and as a means of solving scattering problems by rigid
surfaces in non-uniform flows. The results show that the error associated with
the physical model deteriorates with increasing frequency and mean flow Mach
number. However, the error is generated only in the domain where mean flow
non-uniformities are significant and is constant in regions where the flow is
uniform.
