Model Equations

The chapter begins with the full equations of fluid mechanics for viscous, heat conducting, homogeneous fluids. Exact implicit solutions are developed for plane waves in ideal fluids, as well as an exact nonlinear wave equation for nonplanar waves in a perfect gas. Ordering procedures are introduced that permit structured derivations of approximate wave equations accounting for quadratic nonlinearity in thermoviscous fluids. A second-order wave equation that includes both cumulative and local nonlinear effects is derived, from which are obtained the Westervelt, Burgers, and KZK equations, and a generalized Burgers equation for cylindrical and spherical waves and waves in horns.