A dissipative wave packet approach for unified nonlinear acoustics

Nonlinear acoustic waves are investigated from the viewpoint of a wavepacket. The wavepacket is defined as a portion of a wave that travels at an independent phase speed c = c + flu', where c is the sound speed, ]3 is a constant related to the propagation nonlinearity, and u' is the acoustic particle velocity. During travel the wave distorts during travel because of the nonlinearity, and undergoes absorption due to the effects of viscosity, heat conduction, and relaxation. Some of the most interesting phenomena associated with nonlinear acoustic waves are the result of the combined effects of nonlinear propagation (and the resulting distortion of the wave) and of absorption. These effects are especially at work in shock problems. The mathematical approach begins with the notion of cumulative wave distortion, and its development from a nonlinear wave equation. Novel time domain expressions for acoustic absorption are then developed which are valid for both linear and nonlinear acoustic waves. These theoretical concepts, for nonlinear propagation and for absorption, are then combined into a propagation model which is then evaluated numerically in the spatial domain. Several specific and diverse examples are emphasized, including: pulse selfdemodulation, oceanic parametric sonar, enhancement of ultrasound heating by sound-sound nonlinear interaction, and the formation and evolution of acoustic shoci:s without the need for the so-called equal-area rule in weak shock theory. Experimental data are used to verify both the theory and the computational icsults.