Skip to main content Accessibility help
×
Home

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

  • P. L. Sachdev (a1) and K. R. C. Nair (a1)

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.

Copyright

References

Hide All
Blackstock, D. T.: 1964 Thermovirus attenuation of plane, periodic, finite-amplitude sound waves. J. Acoust. Soc. Am. 36, 534542.
Cole, J. D.: 1951 On a quasi-linear parabolic equation occurring in aerodynamics. Q. Appl. Math. 9, 225236.
Crighton, D. G. & Scott, J. F., 1979 Asymptotic solutions of model equations in nonlinear acoustics. Phil Trans. R. Soc. Lond. A 292, 101134.
Douglas, J. & Jones, B. F., 1963 On predictor–corrector methods for nonlinear parabolic differential equations. J. Soc. Ind. & Appl. Maths 11, 195204.
Enflo, B. O.: 1985 Saturation of a nonlinear cylindric sound wave generated by a sinusoidal source. J. Acoust. Soc. Am. 77, 5460.
Fay, R. D.: 1931 Plane sound waves of finite amplitude. J. Acoust. Soc. Am. 3, 222241.
Fubini, E.: 1935 Anamolie nella propagazione di onde acustache di grande ampiezza. Acta Freq. 4, 530581.
Leibovich, S. & Seebass, A. R. (eds) 1974 Nonlinear Waves. Cornell University Press.
Lesser, M. B. & Crighton, D. G., 1975 Physical acoustics and the method of matched asymptotic expansions. In Physical Acoustics (ed. W. P. Mason & R. N. Thurston), vol. 11. Academic Press.
Lighthill, M. J.: 1956 Viscosity effects in sound waves of finite amplitude. In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davies). Cambridge University Press.
Nair, K. R. C.: 1988 Numerical and analytic studies of generalised Burgers equations. Ph.D. thesis, Indian Institute of Science, Bangalore, India.
Nimmo, J. J. C. & Crighton, D. G. 1986 Geometrical and diffusive effects in nonlinear acoustic propagation over long ranges. Phil. Trans. R. Soc. Lond. A 320, 135.
Parker, D. F.: 1980 The decay of saw-tooth solutions to the Burgers equation. Proc. R. Soc. Lond. A 369, 409424.
Sachdev, P. L.: 1987 Nonlinear Diffusive Waves. Cambridge University Press.
Sachdev, P. L., Tikekar, V. G. & Nair, K. R. C. 1986 Evolution and decay of spherical and cylindrical N waves. J. Fluid Mech. 172, 347371.
Scott, J. F.: 1981 Uniform asymptotics for spherical and cylindrical nonlinear acoustic waves generated by a sinusoidal source. Proc. R. Soc. Lond. A 375, 211230.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

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

  • P. L. Sachdev (a1) and K. R. C. Nair (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed