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

doi:10.1016/j.ijnonlinmec.2012.07.006

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 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 language	English
Pages (from-to)	72-77
Number of pages	6
Journal	International Journal of Non-Linear Mechanics
Volume	48
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2012.07.006
Publication status	Published - Jan 1 2013

Keywords

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

ASJC Scopus subject areas

Mechanics of Materials
Mechanical Engineering
Applied Mathematics

Access to Document

10.1016/j.ijnonlinmec.2012.07.006

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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.",

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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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