A note on acoustic propagation in power-law fluids

Compact kinks, mild discontinuities, and a connection to finite-scale theory

Dongming Wei, P. M. Jordan

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Acoustic traveling waves in a class of power-law viscosity fluids are investigated. Both bi-directional and unidirectional versions of the one-dimensional (1D), weakly non-linear equation of motion are derived; traveling wave solutions (TWSs), special cases of which take the form of compact and algebraic kinks, are determined; and the impact of the bulk viscosity on the structure/nature of the kinks is examined. Most significantly, we point out a connection that exists between the power-law model considered here and the recently introduced theory of finite-scale equations.

Original languageEnglish
Pages (from-to)72-77
Number of pages6
JournalInternational Journal of Non-Linear Mechanics
Volume48
DOIs
Publication statusPublished - Jan 2013
Externally publishedYes

Fingerprint

Power-law Fluid
Kink
Discontinuity
Acoustics
Power Law
Viscosity
Propagation
Bulk Viscosity
Fluids
Acoustic Waves
Traveling Wave Solutions
Nonlinear equations
Traveling Wave
Equations of motion
Equations of Motion
Nonlinear Equations
Fluid
Model
Class
Form

Keywords

  • Finite-scale Navier-Stokes equations
  • Non-linear acoustics
  • Power-law fluids
  • Traveling wave solutions

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Applied Mathematics

Cite this

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AB - Acoustic traveling waves in a class of power-law viscosity fluids are investigated. Both bi-directional and unidirectional versions of the one-dimensional (1D), weakly non-linear equation of motion are derived; traveling wave solutions (TWSs), special cases of which take the form of compact and algebraic kinks, are determined; and the impact of the bulk viscosity on the structure/nature of the kinks is examined. Most significantly, we point out a connection that exists between the power-law model considered here and the recently introduced theory of finite-scale equations.

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