THE SCATTERING OF SOUND-WAVES BY A VORTEX - NUMERICAL SIMULATIONS ANDANALYTICAL SOLUTIONS

The scattering of plane sound waves by a vortex is investigated by sol ving the compressible Navier-Stokes equations numerically, and analyti cally with asymptotic expansions. Numerical errors associated with dis cretization and boundary conditions are made small by using high-order -accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computat ions of flow fields with acoustic waves of amplitude five orders of ma gnitude smaller than the hydrodynamic fluctuations is directly verifie d. The properties of the scattered field are examined in detail. The r esults reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowl y decaying vortex flow field is important. Approximate analytical solu tions that account for the refraction effect are developed and found t o be in good agreement with the computations and experiments.