Index of content:
Volume 129, Issue 2, February 2011
- NONLINEAR ACOUSTICS 
129(2011); http://dx.doi.org/10.1121/1.3531799View Description Hide Description
A model is developed for the propagation of finite amplitude acoustical waves and weak shocks in a straight duct of arbitrary cross section. It generalizes the linear modal solution, assuming mode amplitudes slowly vary along the guide axis under the influence of nonlinearities. Using orthogonality properties, the model finally reduces to a set of ordinary differential equations for each mode at each of the harmonics of the input frequency. The theory is then applied to a two-dimensional waveguide. Dispersion relations indicate that there can be two types of nonlinear interactions either called “resonant” or “non-resonant.” Resonant interactions occur dominantly for modes propagating at a rather large angle with respect to the axis and involve mostly modes propagating with the same phase velocity. In this case, guided propagation is similar to nonlinear plane wave propagation, with the progressive steepening up to shock formation of the two waves that constitute the mode and reflect onto the guide walls. Non-resonant interactions can be observed as the input modes propagate at a small angle, in which case, nonlinear interactions involve many adjacent modes having close phase velocities. Grazing propagation can also lead to more complex phenomena such as wavefront curvature and irregular reflection.
129(2011); http://dx.doi.org/10.1121/1.3531839View Description Hide Description
A theory is developed that allows one to consider the dynamics of an acoustically induced bubble near a fluid layer of finite density and thickness. The theory reveals that, as far as the scattered field of a bubble in the far-field zone is concerned, the layer thickness is a very important factor because the behavior of the scattered field in the cases of infinite and finite layers is qualitatively different even if both layers are of the same density. The amplitude of the scattered pressure from a bubble pulsating in the vicinity of an infinite layer is larger than that for the same bubble in an unbounded fluid, while in the case of a finite layer, on the contrary, the amplitude of the scattered pressure for a bubble near the layer is smaller than that in an unbounded fluid. It is also shown that the higher the layer density, the greater the difference between the scattered pressure amplitudes for infinite and finite layers.