SCATTERING OF SURFACE WAVES BY SUBMERGED CIRCULAR CYLINDERS. PART I: SCATTERING BY TWO CYLINDERS.
STANFORD UNIV CALIF DEPT OF MATHEMATICS
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The paper is concerned with the scattering of small amplitude waves on the surface of an incompressible and inviscid fluid in which a pair of rigid and parallel circular cylinders are wholly immersed. Attention is given to the setting wherein a straight-crested and time-periodic primary wave train advances in a direction normal to the cylinder axes and, in particular, to the characterization of the accompanying reflection and transmission coefficients for the secondary wave trains. If the plane or linearized form of the free surface condition be adopted, resolution of the harmonic boundary value problem thus posed is shown to be equivalent to solving an infinite system of linear equations, and this equivalence is also utilized for theoretical considerations bearing on the existence and uniqueness of solutions. The analysis forms an extension of others which have previously established the absence of reflection for a single submerged cylinder in similar circumstances and reveals that the latter feature does not carry over to the two-cylinder configuration, although the amount of reflection becomes arbitrarily small when the cylinders are sufficiently far apart. Author
- Fluid Mechanics