Abstract
A review of basic linear ocean sound propagation models as derived from fluid dynamics is presented. By retaining nonlinear terms in the equations of fluid dynamics a nonlinear time domain wave equation is then derived. A unidirectional approximation leads to a nonlinear time domain version of the parabolic equation, a nonlinear progressive wave equation (NPE), which can treat propagation of finite amplitude signals in a refracting medium in a wave theoretic sense and hence includes propagation through a caustic. In the limit of infinitesimal acoustics a linear time domain parabolic equation results which can be directly solved numerically without Fourier synthesis. Inserting a harmonic solution into this equation and taking the far field limit reduces this equation to the standard parabolic equation. Linear and nonlinear time domain examples are presented including the propagation of a shock wave through a caustic.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Urick, R. J., Principles of Underwater Sound, 3rd Edition, McGrawHill Book Company, New York, 1983, p. 2.
Lasky, M., “Review of underwater acoustic to 1950,” J. Acoust. Soc. Am. 61, 283–297 (1977).
Pierce, A.D., Acoustics: An Introduction to its Physical Principles and Applications, McGraw-Hill Book Company, New York, 1981, pp. 3–6.
Clay, C. S. and Medwin, H., Acoustical Oceanography, Wiley-Interscience, New York, 1977, pp. 395–404.
McDonald, B. E., and Kuperman, W. A., “Time Domain Solution of the Parabolic Equation Including Nonlinearity,” Proc. Workshop on Comp. Ocean Acoust., Yale Univ. (eds. M. Schultz and D. Lee ), August 1984.
McDonald, B. E., and Kuperman, W. A., “Time Domain Solution of Nonlinear Pulse Propagation,” Proc. NATO Adv. Res. Workshop on Hybrid Formulation of Wave Propagation and Scattering, IAFE, Castel Gandolfo, Italy (ed. L. B. Felson ), Sept. 1983.
McDonald, B. E., and Kuperman, W. A., “Broadband Pulse Propagation in the Time Domain,” Proc. IMACS Symp. on Computing Methods in Ocean Acoustics, Oslo, August 1985.
McDonald, B. E., and Ambrosiano, J., “Higher Order Upwind Flux Methods for Scalar Hyperbolic Conservation Laws,” J. Comp. Phys. 56, 448 (1984).
Kuperman, W. A., and Jensen, F. B., “Deterministic propagation model I Fundemental principles,” in Underwater Acoustics and Signal Processing, edited by Leif Bjorno (D. Reidel Publishing Co., Dordrect, 1980 ).
Jensen, F. B., and Kuperman, W. A., “Consistency tests of acoustic propagation models,” SACLANT ASW Research Centre, La Specia, Italy, SM-157 (1982).
Jensen, F. G., “Numerical Models in Underwater Acoustics,” Proc. NATO Adv. Res. Workshop on Hybrid Formulation of Wave Propagation and Scattering, IAFE, Castel Gandolfo, Italy (ed. L. B. Felsen ), Sept. 1983.
Officer, C. B., Introduction to the Theory of Sound Transmission. ( McGraw-Hill, New York, 1958 ).
Tolstoy, I., and Clay, C. S., Ocean Acoustics: Theory arid Experiment in Underwater Sound. ( McGraw-Hill, New York, 1966 ).
Tucker, D. G., and Gazey, B. K., Applied Underwater Acoustics. (Pergamon Oxford, 1966 ).
Tolstoy, I., Wave Propagation. ( McGraw-Hill, New York, 1973 ).
Urick, R. J., Principles of Underwater Sound. ( McGraw-Hill, New York, 1975 ).
Clay, C. S., and Medwin, H., Acoustical Oceanography. ( Wiley-Interscience, New York, 1977 ).
Keller, J. B., and Papadakis, J. S., (eds.) Wave Propagation and Underwater Acoustics. ( Springer-Verlag, Berlin, 1977 ).
De Santo, J. A., (ed.), Ocean Acoustics. ( Springer-Verlag, Berlin, 1979 ).
Brekhovskikh, L. M., Wave in Layered Media. ( Academic, New York, 1980 ).
Brekhovskikh, L. M., and Lysanov, Yu, Fundamentals of Ocean Acoustics. ( Springer-Verlag, Berlin, 1982 ).
DiNapoli, F. R., and Deavenport, R. L., “Theoretical and numerical Green’s function field solution in plane multilayered medium,” J. Acoust. Soc. Am. 67, 92–105, (1980).
Kutschale, H. W., “Rapid computation by wave theory of propagation loss in the Arctic Ocean,” Rpt. CU-8-73, Columbia University, Palisades, N. Y., (1973).
Schmidt, H., and Jensen, F. B., “Efficient numerical solution technique for wave propagation in horizontally stratified ocean environments,” Rpt. SM-173, SACLANT ASW Research Centre, La Specia, Italy (1984).
Evans, R. B., “A coupled mode solution for acoustic propagation in a waveguide with stepwise depth variations of a penetrable bottom,” J. Acoust. Soc. Am., 74, 188–195 (1983).
Tappert, F. D., “The parabolic Approximation method,” in J. B. Keller and J. S. Papadakis, Ed., Wave Propagation and Underwater Acoustics, Springer-Verlag, Berlin, 1977, pp. 224–287.
Jensen, F. B., and Krol, H. R., “The use of the parabolic equation method in sound propagation modelling,” Rpt. SM-72, SACLANT ASW Research Centre, La Specia, Italy (1975).
Davis, J. A., White, D., and Cavanagh, R. C., “NORDA parabolic equation workshop,” Rpt. TN-143, Naval Ocean Research and Development Activity, NSTL Stn, MS (1982).
Lee, D., and Gilbert, K. E., “Recent progress in modeling bottom interacting sound propagation with parabolic Equations,” in Ocean 82 Conference Record (MTS-IEEE, Washington, D. C. 1982 ), pp. 172–177.
Rogers, P. H., and Gardner, J. H., “Propagation of Sonic Booms in the Thermosphere,” J. Acoust. Soc. Am. 67, 78–91 (1980).
McDonald, B. E., and Ambrosiano, J., “Self-Similar Solution for Spherical Weak Shocks,” J. Acoust. Soc. Am. Suppl. 1, Vol. 77 (1985).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Plenum Press, New York
About this chapter
Cite this chapter
Kuperman, W.A., McDonald, B.E. (1986). Linear and Nonlinear Ocean Acoustic Propagation Models. In: Akal, T., Berkson, J.M. (eds) Ocean Seismo-Acoustics. NATO Conference Series, vol 16. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2201-6_12
Download citation
DOI: https://doi.org/10.1007/978-1-4613-2201-6_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9293-7
Online ISBN: 978-1-4613-2201-6
eBook Packages: Springer Book Archive