# Peter and Meylan 2004

Malte A. Peter and Michael H Meylan, Infinite depth interaction theory for arbitrary
bodies with application to wave forcing of ice floes,
*J. of Fluid Mechanics.*,
**500**,
pp 145-167.

This paper extended Kagemoto and Yue Interaction Theory to infinite depth and also present the fomulation in a complete manner (treating bodies of arbitrary geometery for example).

## Abstract

We extend the finite-depth interaction theory of Kagemoto and 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 and 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.

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