Advertisement

A New Form of the Wave Equation for Sound in a General Layered Fluid

  • O. A. Godin

Abstract

By introduction of a new vertical coordinate, the wave equation in a layered medium is transformed into the reduced wave (Helmholtz) equation. In the new form of the wave equation, effects of gravity as well as of density and of mean current stratification appear only in the effective wave number and in the transformation of the variable used. Starting from this equation, a number of new results are obtained. Some applications to three-dimensionally varying media are considered. The equation of sound propagation in an ocean with arbitrarily slow mean currents is obtained and the corresponding parabolic approximation is discussed.

Keywords

Wave Equation Parabolic Equation Layered Medium Sound Propagation Mesoscale Eddy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramovitz, M., and Stegun, I.A., eds., 1964, “Handbook of Mathematical Functions”, National Bureau of Standards.Google Scholar
  2. Boyles, C.A., 1984, “Acoustic Waveguides. Applications to Oceanic Science”, John Wiley and Sons, New York etc.Google Scholar
  3. Brekhovskikh, L.M., 1980, “Waves In Layered Media”, Academic Press, New York.zbMATHGoogle Scholar
  4. Brekhovskikh, L.M., and Lysanov, Yu., 1982, “Fundamentals of Ocean Acoustics”, Springer-Verlag, Berlin etc.Google Scholar
  5. Chunchuzov, I.P., 1985, “Field of a Point Sound Source in an Atmospherical Layer Close to the Earth”, Sov. Phvs. Acoust., 31: N1.Google Scholar
  6. DeSanto, J.A., 1979, “Theoretical Methods In Ocean Acoustics”, in: “Ocean Acoustics”, J.A. DeSanto, ed., Springer-Verlag, Berlin etc.Google Scholar
  7. Fabricant, A.L., 1976, “Resonance Interaction of Sound Waves With Stratified Flow”, Sov. Phvs. Acoust., 22: N1.Google Scholar
  8. Godin, O.A., 1980, “On Reflection of Plane Waves From A Layered Half-Space”, Dokl. AN SSSR, 255: 1069. (In Russian)MathSciNetGoogle Scholar
  9. Godin, O.A., 1985a, “Reciprocity Relations for Acoustic-Gravity Waves”, in: “Wolny i Difraktzia 85”, v. 1, TGU Tbilisi. ( In Russian )Google Scholar
  10. Godin, O.A., 1985b, “On a Modification of the Wave Equation for a Layered Medium”, Wave Motion, 7: 515.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Godin, O.A., 1986, “A Modification of the Sound Propagation Equation For a Layered Medium”, in: “Ocean Acoustics. 1984”, Nauka, Moscow. (In Russian)Google Scholar
  12. Goldstein, M.E., 1976, “Aeroacoustics”, McGraw-Hill, New York etc.zbMATHGoogle Scholar
  13. Grigor’eva, N.S., and Yavor, M.I., 1986, “Method of Normal Modes for Acoustic Field Calculation in an Oceanic Waveguide Perturbed by a Current”, Sov. Phys. Acoust., 32: N1.Google Scholar
  14. Itzikowitz, S., Jacobson, M.J.m and Siegmann, W.L., 1983 “Modeling of Long-Range Acoustic Transmission Through Cyclonic and Anticyclonic Eddies”, J. Acoust. Soc. Amer., 73: 1556.ADSCrossRefGoogle Scholar
  15. Krasnushkin, P.E., 1980, “A Method of Recursive Impedance Calculation in Wave Problems in Elastic Media”, Dokl. AN SSSR, 252: 332. (In Russian)MathSciNetGoogle Scholar
  16. Lan, N.P., and Tappert, F.D., 1985, “Parabolic Equation Modelling of the Effects of Ocean Currents on Sound Transmission”, J. Acoust. Soc. Amer., 78: 642.ADSCrossRefGoogle Scholar
  17. Lee D., Botseas, G., and Papadakis, J.S., 1981, “Finite-Difference Soultion to the Parabolic Wave Equation”, J. Acoust. Soc. Amer., 70: 795.MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. Lyamshev, L.M., 1981., “On Definition of Impedance in Acoustics of Moving Media”, Dokl. AN SSSR. 261:74. (In Russian)Google Scholar
  19. Newhall, B.K., Jacobson, M.J., and Siegmann, W.L., 1980, “Effect of a Class of Random Currents on Acoustic Transmission in an Ocean with Linear Sound Speed”, J. Acoust. Soc. Amer., 67:1997.ADSzbMATHCrossRefGoogle Scholar
  20. Obukhov, A.M., 1943, “On Sound Wave Propagation in a Vortex Flow”, Dokl. AN SSSR, 39: 46. (In Russian)MathSciNetGoogle Scholar
  21. Ostashev, V.E., 1984, “Wave Description of Sound Propagation in a Startified Moving Atmosphere”, Sov. Phys. Acoust., 30: N4.Google Scholar
  22. Polyanskaya, V.A., 1985, “On the Effect of a Currents Velocity Field on Sound Propagation in the Ocean”, Sov. Phys. Acoust., 31: N5.MathSciNetGoogle Scholar
  23. Robertson, J.S., Siegmann, W.L., and Jacobson, M.J., 1985, “Current and Current Shear Effects in the Parabolic Approximation”, J. Acoust. Soc. Amer., 77: 1768.ADSzbMATHCrossRefGoogle Scholar
  24. Steinmetz, G.G., and Singh, J.J., 1972, “Reflection and Transmission of Acoustical Waves From a Layer with Space-Dependent Velocity”, J. Acoust. Soc. Amer., 51: 218.ADSCrossRefGoogle Scholar
  25. Tatarskii, V.I., 1971, “The Effects of the Turbulent Atmosphere on Wave Propagation”, Sect. 34, Jerusalem.Google Scholar
  26. Tatarskii, V.I., 1979, “To the Theory of Sound Propagation in a Stratified Atmosphere”, Izv. Atmospher. Ocean. Sci., 15: N11.Google Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • O. A. Godin
    • 1
  1. 1.P.P. Shirshov Institute of Oceanologythe USSR Academy of SciencesMoscowUSSR

Personalised recommendations