Infinite-depth interaction theory for arbitrary floating bodies applied to wave forcing of ice floes

Abstract

We extend the finite-depth interaction theory of Kagemoto & Yue(1986) to water of infinite depth and bodies of arbitrary geometry. The sum over the discrete roots of the dispersion equation in the finite-depth theory becomes an integral in the infinite-depth theory. This means that the infinite dimensional diffraction transfer matrix in the finite-depth theory must be replaced by an integral operator. In the numerical solution of the equations, this integral operator is approximated by a sum and a linear system of equations is obtained. We also show how the calculations of the diffraction transfer matrix for bodies of arbitrary geometry developed by Goo & Yoshida (1990) can be extended to infinite depth, and how the diffraction transfer matrix for rotated bodies can be calculated easily. This interaction theory is applied to the wave forcing of multiple ice floes and a method to solve the full diffraction problem in this case is presented. Convergence studies comparing the interaction method with the full diffraction calculations and the finite- and infinite-depth interaction methods are carried out.