Acoustic shock and acceleration waves in selected inhomogeneous fluids

Acoustic shock and acceleration waves in inhomogeneous fluids are investigated using both analytical and numerical methods. In the context of start-up signaling problems, and based on linear acoustics theory, we study the propagation of such waveforms in the atmosphere and in fluids that possess a periodic ambient density profile. It is shown that vertically-running shock and acceleration waves in the atmosphere suffer amplitude growth. In contrast, those in the periodic-density fluid have bounded amplitudes that exhibit periodic, but non-trivial, oscillations; this is illustrated via a series of numerically-generated profile-evolution plots, which were computed using the PyClaw software package.