Vortical perturbations in shear flow, scattered at a hard wall : pressure release wall transition

An analytically exact solution for the problem of low Mach number (i.e. incompressible) incident vorticity scattering at a hard - to - pressure release (Z = 0 ) wall transition is obtained using the Wiener-Hopf method. Harmonic vortical perturbations of inviscid linear shear flow are scattered at the wall transition, which results in a pressure-velocity field which is qualitatively different for low shear and high shear cases. The incompressible field produces an acoustic outer field, which can be determined for the low shear case, including a $U^4_0$ relation for the radiated power. The similar behaviour of this Z = 0 solution when compared with the asymptotic behaviour of the solution for finite impedance case confirms the validity of this last solution.