The effects of coupling on finite-amplitude acoustic traveling waves in thermoviscous gases: Blackstock's models

P. M.  Jordan

doi:10.3934/eect.2016010

Article Contents

2016, Volume 5, Issue 3: 383-397. Doi: 10.3934/eect.2016010

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The effects of coupling on finite-amplitude acoustic traveling waves in thermoviscous gases: Blackstock's models

P. M. Jordan^1,

1.
Acoustics Division, U.S. Naval Research Laboratory, Stennis Space Center, MS 39529

Received: April 30, 2016

Revised: April 30, 2016

Published: August 2016

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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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Mathematics Subject Classification: Primary: 74J30, 76N15, 80A20; Secondary: 35M30.

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