Linear Wave Interaction by Multiple Vertical Cylinders of Non-Circular Smooth Cross-Section: an Iterative-Asymptotic Approach

Abstract

The three-dimensional problem of water wave diffraction by multiple cylinders of non-circular smooth cross-sections is studied. The rigid cylinders extend from the sea bottom to the free surface in water of finite depth. The flow is described by the linear theory of potential flow. A fourth-order asymptotic solution of the diffraction problem by a single cylinder with the asymptotic parameter being the closeness of the cross-section to a circle is combined with an iterative method to consider the effect of the wave interaction between the cylinders. The original problem for non-circular cylinders is reduced to a set of diffraction and radiation problems for circular cylinders at each asymptotic order. The velocity potentials are given by their Fourier series, and the problem solving is simplified to the algebraic operations involving the Fourier coefficients of the potentials and the shape function, which describes the cross-sectional shape of the vertical cylinder. The hydrodynamic forces and wave run-up values for geometries of two elliptical and four nearly square cylinders are presented for a range of incident wave frequencies and angles of attack. The method is validated by comparing the present hydrodynamic force results with the ones in the literature, and good agreement is reported. © 2024 Elsevier Ltd