Progressive Waves in Lossless and Lossy Fluids

This chapter analyzes nonlinear progressive waves, and primarily plane waves. Following presentation of exact implicit solutions for ideal fluids, approximate explicit solutions are obtained for harmonic generation in lossless and lossy fluids. The Rankine-Hugoniot relations are derived for shocks of arbitrary strength, followed by their quadratic approximation for weak shocks. The history and solutions of the Burgers equation are presented, including the rise time and thickness of weak shocks. Progressive plane-wave solutions based on weak-shock theory are transformed to describe cylindrical and spherical waves and waves in horns. Expressions for the intensity and absorption of finite-amplitude waves are obtained.