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SCATTERING OF SURFACE WAVES BY SUBMERGED CIRCULAR CYLINDERS. PART II. SCATTERING BY AN INFINITE ARRAY OF CYLINDERS.
STANFORD UNIV CALIF DEPT OF MATHEMATICS
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The paper deals with progressive surface wave motions of a small amplitude and time-periodic nature in an ideal fluid which contains an infinite submerged array of parallel and identical circular cylinders. Their characterization is sought in the framework of a homogeneous linear boundary value problem for harmonic functions which exhibit a common phase shift that plays the role of an eigenvalue for any displacement along the direction of wave propagation with a magnitude equal to the separation between adjacent cylinders. An equivalent integral equation is formulated and reduced to an infinite homogeneous linear system from which there obtains a determinantal condition that specifies the dependence of the eigenvalue, or effective wave number, on the frequency, gravitation constant, and geometric parameters. Approximations to the eigenvalue are calculated for any fixed wave length when 1 the radius of the cylinders is small compared with their spacing or 2 their separation distance is large with respect to the radius and depth of immersion. Author
APPROVED FOR PUBLIC RELEASE