Diffraction of an impulsive line source with wake

The problem of diffraction due to an impulse line source by an absorbing half-plane with wake using Myres' impedance condition (Myers 1980 J. Sound Vib. 71 429-34) in the presence of a subsonic fluid flow is studied. The time dependence of the field requires a temporal Fourier transform in addition to the spatial Fourier transform. The solution of the problem in the presence of wake is obtained by using Greens' function method, Fourier transform, the Wiener-Hopf technique and the modified stationary phase method. Expressions for the total far field for the trailing edge (wake present) situation are given. It is observed that the field produced by the Kutta-Joukowski condition will be substantially in excess of the field when this condition is ignored. Finally, a simple procedure is devised to calculate the inverse temporal Fourier transform. The solution for the leading edge situation can be obtained if the wake, and consequently a Kutta-Joukowski edge condition, is ignored. This can also be seen from the numerical results.