The solution to water wave scattering and radiation problems involving semi-immersed circular cylinders


by R. Porter


In this technical report we describe the method of solution to a variety of twodimensional problems involving semi-immersed cylinders in the free surface. These include: (i) determining the reflection and transmission coefficients for the scattering of incident waves by a single fixed cylinder; (ii) determining the added mass and radiation damping for a cylinder forced to move with unit velocity in both heave and sway motions; (iii) determining the heave and sway added mass and damping coefficients for a cylinder in forced motion next to a vertical boundary on which either a Neumann or Dirichlet condition is posed, equivalent to a pair of cylinders forced to move in-phase or out of phase with each other. In each case, the fluid is assumed to be of infinite depth and the fluid motion is two-dimensional. The description of the method of solution for parts (i) and (ii) follows that of Martin & Dixon (1983). The formulation of the solution for the final third problem is similar to that performed by Wang & Wahab (1971) for catamarans in heave oscillation only.

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