UACE2017 Proceedings: Simple test cases with accurate numerical solutions for 3-D sound propagation modelling

• Session:
  Three-dimensional sound propagation models and effects
• Paper:
  Simple test cases with accurate numerical solutions for 3-D sound propagation modelling
• Author(s):
  Sven Ivansson
• Abstract:
  Modelling of sound propagation from a point source in media with azimuthal variations of bathymetry and/or sound speed is computationally challenging. The parabolic equation (PE) method is useful, but it entails approximations and verification by other methods is needed. By comparison with solutions by image source and adiabatic mode PE techniques, it has been realized in recent years that incorporation of a leading-order cross-derivative term in the PE square-root operator approximation is sometimes needed. Test cases of wedge and canyon type have been used, with medium variations in only one of the two horizontal Cartesian coordinates. For such media, the point-source solution can be expressed as an integral of solutions of an ensemble of 2-D problems. These 2-D problems can be solved by coupled modes, for example. In the present paper, a particular type of such test cases is considered. In essence, the difference of inverse squared sound speed at two arbitrary horizontal positions does not depend on depth. It follows that only the modal wavenumbers depend on horizontal position, not the mode shapes. The pertinent ensemble of 2-D problems can be solved separately for each mode, and the "adiabatic approximation" is thus exact. Direct propagator-matrix multiplication, from opposite horizontal directions with matching at the source range, is applied to obtain explicit solutions in terms of exponential and Airy functions, and the pertinent integral is computed with error control using adaptively determined step lengths. Two specific examples are studied in detail, one of "wedge" type and one of "canyon" type. Despite the simplifications made, allowing very accurate numerical solutions, clear mode-dependent effects of horizontal refraction are obtained and compared to modal ray diagrams. Comparisons with 3-D PE results are under way.
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Contact details

• Contact person:
  Dr Sven Ivansson
• e-mail:
  
• Affiliation:
  Swedish Defence Research Agency
• Country:
  Sweden