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Evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source

Published online by Cambridge University Press:  26 April 2006

P. L. Sachdev  and
K. R. C. Nair
P. L. Sachdev
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore-560012, India
K. R. C. Nair
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore-560012, India
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Abstract

The present work gives a comprehensive numerical study of the evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source. Using pseudospectral and predictor–corrector implicit finite difference methods, we first reproduced the known analytic results of the plane harmonic problem to a high degree of accuracy. The non-planar harmonic problems, for which the amplitude decay is faster than that for the planar case, are then treated. The results are correlated with the known asymptotic results of Scott (1981) and Enflo (1985). The constant in the old-age formula for the cylindrical canonical problem is found to be 1.85 which is rather close to 2, ‘estimated’ analytically by Enflo. The old-age solutions exhibiting strict symmetry about the maximum are recovered; these provide an excellent analytic check on the numerical solutions. The evolution of the waves for different source geometries is depicted graphically.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 389 - 404
Copyright
© 1989 Cambridge University Press

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