Nonlinear sound–vortex interactions in an inviscid isentropic fluid: A two-fluid model

A new two-fluid model is developed to describe the nonlinear interaction of acoustic waves and vortices. Analytical and computational results are presented for a sound pulse interacting with and being modified by a vortex. A novel numerical method based on a particle-in-cell discretization of the acoustic field is developed and used to study the nonlinear scattering of sound by a cylindrical vortex. Equations for the sound wave packet propagating in an axially symmetric mean flow are integrated analytically. Nonlinear modification of the vortex flow by the high-frequency sound is found to be mediated by growing pressure disturbances generated by the radiative forcing on the high gradient regions of the acoustic pulse. The total energy of the vortex mean flow grows monotonically, as the acoustic component loses its energy. The changes in the kinetic and internal energies of the vortex are greater than the changes in its total energy, although these changes are reversible in lowest order of the nonlinear vortex–acoustic interaction.