Index of content:
Volume 127, Issue 2, February 2010
- NONLINEAR ACOUSTICS 
127(2010); http://dx.doi.org/10.1121/1.3277202View Description Hide Description
For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elasticwave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine–Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell–Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.
127(2010); http://dx.doi.org/10.1121/1.3277190View Description Hide Description
The nonlinear propagation through porous media is investigated in the framework of Biot theory. For illustration, and considering the current interest for the determination of the elastic properties of granular media, the case of nonlinear propagation in “model” granular media (disordered packings of noncohesive elastic beads of the same size embedded in a visco-thermal fluid) is considered. The solutions of linear Biot waves are first obtained, considering the appropriate geometrical and physical parameters of the medium. Then, making use of the method of successive approximations of nonlinear acoustics, the solutions for the second harmonic Biot waves are derived by considering a quadratic nonlinearity in the solid frame constitutive law (which takes its origin from the high nonlinearity of contacts between grains). The propagation in a semi-infinite medium with velocity dispersion, frequency dependent dissipation, and nonlinearity is first analyzed. The case of a granular medium slab with rigid boundaries, often considered in experiments, is then presented. Finally, the importance of mode coupling between solid and fluid waves is evaluated, depending on the actual fluid, the bead diameter, or the applied static stress on the beads. The application of these results to other media supporting Biot waves (porous ceramics, polymer foams, etc.) is straightforward.
127(2010); http://dx.doi.org/10.1121/1.3279793View Description Hide Description
The problem of acoustic microstreaming that develops around a gas bubble in an ultrasound field is considered. It is shown that the solutions obtained previously by Wu and Du [(1997). J. Acoust. Soc. Am.101, 1899–1907], which are based on the assumption that viscous effects are essential only within a thin boundary layer while beyond the boundary layer the liquid can be considered to be inviscid, lead to a severe underestimation of the power of acoustic streaming. An improved theory is suggested that corrects the errors of the previous theory and extends its limits. The proposed theory treats the entire bulk of the liquid outside the bubble and the gas inside the bubble as viscous heat-conducting fluids. No restrictions are imposed on the size of the bubble relative to the viscous, thermal, and sound wavelengths in the ambient liquid and those in the internal gas medium. All modes of the bubble’s motion (volume pulsation, translation, and shape oscillations) are taken into account. Expressions for the radial and tangential stresses produced by the acoustic streaming are also derived. Numerical examples for parameters of interest are presented.