Old-age behaviour of cylindrical and spherical nonlinear waves: Numerical and asymptotic results

P. W. Hammerton; David George Crighton

doi:10.1098/rspa.1989.0036

Old-age behaviour of cylindrical and spherical nonlinear waves: Numerical and asymptotic results

P. W. Hammerton, David George Crighton

Fluids & Structures

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Abstract

Asymptotic and numerical analyses are presented for the nonlinear evolution of cylindrical and spherical acoustic waves subject to thermoviscous dissipation. Old-age asymptotic solutions of generalized Burgers equations are obtained for initially discontinuous profiles. These solutions and the underlying asymptotic structure are completely validated by the numerical results. For cylindrical geometry the numerical analysis supplements the asymptotic analysis by providing numerical amplitude coefficients that were previously undetermined.

Original language	English
Pages (from-to)	387-405
Number of pages	19
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	422
Issue number	1863
DOIs	https://doi.org/10.1098/rspa.1989.0036
Publication status	Published - 8 Apr 1989

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10.1098/rspa.1989.0036

Cite this

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title = "Old-age behaviour of cylindrical and spherical nonlinear waves: Numerical and asymptotic results",

abstract = "Asymptotic and numerical analyses are presented for the nonlinear evolution of cylindrical and spherical acoustic waves subject to thermoviscous dissipation. Old-age asymptotic solutions of generalized Burgers equations are obtained for initially discontinuous profiles. These solutions and the underlying asymptotic structure are completely validated by the numerical results. For cylindrical geometry the numerical analysis supplements the asymptotic analysis by providing numerical amplitude coefficients that were previously undetermined.",

author = "Hammerton, {P. W.} and Crighton, {David George}",

year = "1989",

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language = "English",

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publisher = "The Royal Society",

number = "1863",

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T1 - Old-age behaviour of cylindrical and spherical nonlinear waves: Numerical and asymptotic results

AU - Hammerton, P. W.

AU - Crighton, David George

PY - 1989/4/8

Y1 - 1989/4/8

N2 - Asymptotic and numerical analyses are presented for the nonlinear evolution of cylindrical and spherical acoustic waves subject to thermoviscous dissipation. Old-age asymptotic solutions of generalized Burgers equations are obtained for initially discontinuous profiles. These solutions and the underlying asymptotic structure are completely validated by the numerical results. For cylindrical geometry the numerical analysis supplements the asymptotic analysis by providing numerical amplitude coefficients that were previously undetermined.

AB - Asymptotic and numerical analyses are presented for the nonlinear evolution of cylindrical and spherical acoustic waves subject to thermoviscous dissipation. Old-age asymptotic solutions of generalized Burgers equations are obtained for initially discontinuous profiles. These solutions and the underlying asymptotic structure are completely validated by the numerical results. For cylindrical geometry the numerical analysis supplements the asymptotic analysis by providing numerical amplitude coefficients that were previously undetermined.

U2 - 10.1098/rspa.1989.0036

DO - 10.1098/rspa.1989.0036

M3 - Article

VL - 422

SP - 387

EP - 405

JO - Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences

SN - 1364-5021

IS - 1863

ER -