The WKB method applied to the reflectiontransmission by a depth-varying random distribution of cylinders in a fluid slab-like region
This paper deals with multiple scattering by a random arrangement of parallel circular elastic cylinders immersed in a fluid. The cylinders are distributed in a region called « slab » that is located between two parallel planes orthogonal to a given x-direction. The disorder inside the slab is not uniform but depends on the x-variable. The goal is to calculate the reflection and transmission coefficients by this space-varying slab. The spatial variations of the random distribution are assumed smooth enough in order to use the WKB (Wentzel-Kramers-Brillouin) method. For this method, a crucial point is the knowledge of the boundary conditions at the interfaces between the homogeneous fluid and the space-varying slab. These boundary conditions are shown to be the usual continuity of pressure and normal displacement. The relation between pressure and normal displacement is given by Euler’s equation and the introduction of an effective mass density.
KeywordsTransmission Coefficient Multiple Scattering Normal Displacement Impedance Ratio Homogeneous Fluid
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