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

P. W. Hammerton, David George Crighton

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)387-405
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1863
Publication statusPublished - 8 Apr 1989

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