Abstract
We consider the propagation of acoustic and thermal waves in classical perfect gases under a coupled, weakly-nonlinear system first derived by Blackstock. Our primary aim is to ascertain the usefulness of Blackstock's system as an approximate model of nonlinear acoustic phenomena. Working in the context of the piston problem, and using a solvable special case of the Navier--Stokes--Fourier system as our benchmark, we compare Blackstock's system against a simpler weakly-nonlinear model whose constitute equations are not coupled. In particular, traveling wave solutions (TWS)s are determined, the structure of the solution profiles is analyzed, numerical comparisons are presented, and follow-on studies are suggested.
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