On the emission of sound by an ionized inhomogeneity

Abstract

The emission (including generation, propagation, scattering, convection and radiation) of sound by an ionized inhomogeneity in a non-uniform mean flow is studied as an extension of the hydrodynamic problem (Howe 1975a, b) to include a variable electromagnetic field. The stagnation enthalpy is the thermodynamic function of state taken as the acoustic variable, and satisfies an inhomogeneous wave equation, which describes the propagation and generation of sound in a compressible mean flow, and which assumes a simplified form at low Mach numbers. The effective acoustic source consists of two dipoles, associated with the Laplace-Lorentz (or electromagnetic) force and the hydrodynamic force. The latter consists of displacement and vortical terms that are shown to be analogous to the classical electric and magnetic forces, respectively. The level of radiation depends on the changes of the activity (work per unit time) of these forces experienced by the ionized inhomogeneity, e.g. as it is convected past electrified bodies, which are responsible for the variable hydrodynamic and electromagnetic fields, and also scatter the wave field. By taking as an example a model problem featuring biaxial symmetry, the amplitude and shape of sound pulses are discussed and illustrated in a number of generation conditions, hydrodynamic and electromagnetic, and observation positions in the far-field. In principle there can be destructive interference between hydrodynamic and electromagnetically generated sound, although in practice this is not expected to occur. In aerodynamic and atmospheric conditions the hydrodynamic sound predominates, whereas in plasma and stellar situations, electromagnetic sound may be dominant.