Farfield viscous effects in nonlinear noise propagation

Abstract

The method of parametric differentiation has been applied to predict the farfield noise propagation in both a lossless and a dissipative medium. The classical nonlinear acoustical problems of calculating the sound field of two rectilinear vortices rotating about an axis between them in a lossless medium and of calculating the sound field generated by a rotating cylinder in a viscous medium have been investigated. Solutions to these classical problems valid for asymptotically small Mach number have been extended to larger values of the Mach number parameter. It is shown that in the lossless medium, the governing equation transformed to parameter space reduces to a wave equation in the farfield. In the dissipative medium, the system of nonlinear partial differential equations transformed to parameter space reduces to a linear partial differential equation of the propagating type which contains a third-order derivative as well as the wave operator. Pressure distributions in the farfield are obtained in the lossless medium; the results appear reasonable physically and mathematically self-self-consistent. The method of parametric differentiation and Newton's method are compared.