UACE2017 Proceedings: Whispering gallery waves in horizontal plane near the curved isobaths in shallow water

• Session:
  Three-dimensional sound propagation models and effects
• Paper:
  Whispering gallery waves in horizontal plane near the curved isobaths in shallow water
• Author(s):
  Boris Katsnelson, Pavel Petrov
• Abstract:
  The horizontal refraction phenomena (or 3D effects) in a shallow-water waveguide with the bottom relief featuring curved isobaths is studied. This situation can be met in areas of a coastal slope that are characterized by curvilinear coastal line, e.g. lagoons and bays, as well as in lakes. Typical curvature radius of isobaths can be estimated for the bathymetry data, and usually amounts to few kilometers. It is shown that for amplitudes of normal modes, describing distribution of acoustic pressure in horizontal plane, under certain conditions whispering gallery waves can exist. The energy of these waves is concentrated in the neighborhood of horizontal rays propagating along the isobath. A relation between the waveguide parameters ensuring the whispering gallery formation is derived. It involves the bottom slope angle, the isobaths curvature, and the water-bottom sound speed ratio. The derived relation is validated by the direct computation of the low frequency acoustic field due to a point source in a cylindrically-symmetric lake. The computation is based on a semi-analytical solution of the adiabatic horizontal refraction equations for the modal amplitudes. This solution is obtained via the separation of variables in the polar coordinate system. Results of numerical calculations are compared with solution using ray approximation in horizontal plane (vertical modes and horizontal rays approach)The possibility of excitation and observation of the whispering gallery waves (modes) in realistic shallow-water waveguides is discussed, and the respective simulation results are presented
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Contact details

• Contact person:
  Prof Boris Katsnelson
• e-mail:
  
• Affiliation:
  Dept of Marine Geosciences
• Country:
  Israel