Publications
Acoustic Wave Equations for a Linear Viscous Fluid and An Ideal Fluid
The mathematical description of acoustic wave propagation within a time- and space-varying, and moving, linear viscous fluid is formulated as a system of coupled linear equations. This system is rigorously developed from fundamental principles of continuum mechanics (conservation of mass, balance of linear and angular momentum, balance of entropy) and various constitutive relations (for stress, entropy production, and entropy conduction) by linearizing all expressions with respect to the small-amplitude acoustic wavefield variables. A significant simplification arises if the fluid medium is neither viscous nor heat conducting (i.e., an ideal fluid). In this case the mathematical system can be reduced to a set of five, coupled, first-order partial differential equations. Coefficients in the systems depend on various mechanical and thermodynamic properties of the ambient medium that supports acoustic wave propagation. These material properties cannot all be arbitrarily specified, but must satisfy another system of nonlinear expressions characterizing the dynamic behavior of the background medium. Dramatic simplifications in both systems occur if the ambient medium is simultaneously adiabatic and stationary.