Acoustic shock and acceleration waves in selected inhomogeneous fluids

TL;DR

This paper investigates how acoustic shock and acceleration waves propagate in inhomogeneous fluids like the atmosphere and periodic-density fluids, revealing different amplitude behaviors through analytical and numerical methods.

Contribution

It provides new insights into wave behavior in inhomogeneous fluids using combined analytical and numerical approaches, including the application of PyClaw software.

Findings

Shock waves in the atmosphere grow in amplitude.

Waves in periodic-density fluids have bounded, oscillatory amplitudes.

Numerical simulations illustrate complex wave evolution patterns.

Abstract

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.