Abstract:
In many aero- and environmental-acoustic problems, convection of sound waves is handled by appropriately increasing or decreasing the local speed of sound and then solving the resulting Helmholtz equation. Such solutions are typically obtained via integral transforms or geometrical acoustics. An exact solution technique that properly incorporates the vector character of mean-flow convection has been found [L. Nijs and C. P. A. Wapenaar, J. Acoust. Soc. Am. 87, 1987--1998 (1987)]. Unfortunately, the formal and numerical complexity of these techniques has prevented detailed comparisons of the acoustic field variables with and without the standard approximation. Results and comparisons for approximate and exact treatment of convection will be presented from a series of simple computations made directly from the linearized time- and space-dependent equations of inviscid fluid motion. Specifically, the propagation of initially plane acoustic waves in a simple shear flow has been addressed to determine how: (i) wavefront orientation and location, (ii) acoustic-particle-velocity vector direction, and (iii) acoustic wave strength compare when mean flow convection is handled approximately and exactly. [Work supported by Ford Motor Company.]