Scattering of low-frequency sound by infinite fluid and solid cylinder
Baynes, Alexander B.
Godin, Oleg A.
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Wave scattering by obstacles is typically studied assuming plane wave incidence. However, full Green?? functions are necessary for problems where the separation of the scatterer from sources, interfaces, or other scatterers is comparable to the dimensions of the scatterer itself. In this paper, the two-dimensional problem of scattering of monochromatic cylindrical waves due to infinite cylinder embedded in a homogeneous fluid is considered. Fluid and solid cylinders are studied, and soft and hard cylinders are revisited. The exact solutions for the Green?? functions are expressed as an infinite series of cylindrical functions with complex amplitudes determined by the acoustic boundary conditions at the surface of the cylinder. Here, we derive closed-form asymptotics for the scattered field in the regime when the scatterer dimensions are small compared to wavelength, i.e., Rayleigh scattering. The scattered wave approximation is valid for arbitrary source and observation points outside the scatterer and is expressed as a simple sum of fields due to three image sources. Image source solutions were anticipated due to classically studied electrostatic analog problems involving dielectric cylinders. Image source representation allows physical insight into the scattering physics and suggests simple yet accurate analytic solutions to interface and waveguide scattering problems.
The article of record as published may be found at http://dx.doi.org/10.1121/1.5036150
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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Baynes, Alexander B. (Monterey, CA; Naval Postgraduate School, 2018-06);This dissertation considers the two-dimensional problem of the scattering of a monochromatic cylindrical wave by an infinite cylinder embedded in a homogeneous fluid. The exact solution is expressed as an infinite series ...
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Baynes, Alexander B.; Godin, Oleg A. (2017);Rayleigh scattering, in which the wavelength is large compared to the scattering object, is usually studied assuming plane incident waves. However, full Green?? functions are required in a number of problems, e.g., when a ...