Added Mass and Damping for Ice Floes by Long Water Wave Theory
Authors: Luk Chih Hung 
Published: October 2008

ABSTRACT
Added mass and damping for ice floes are important parameters in determining floe collision forces with arctic structures. They are measures of the hydrodynamic resistance to the change of the floemotion. This paper presents an analytical approach based on long water wave theory to determine (1) the added mass and damping for a circular ice floe for awide frequency range and with general floe movements including two translations (surge and heave) and one rotation (pitch), and (2) the hydrodynamic impulse function on a circular ice floe resulting from its impact with a rigid structure. The governing equations were solved by (1) the Fourier transformation or(2) the Laplace transformation method, depending on the problem. Closed-form solutions and plots are provided for estimating the added mass, damping, and the hydrodynamic impulse function for a circular ice floe.

INTRODUCTI ON
Ice force resulting from a large ice floe interacting with a stationary structure is an important design consideration for the construction of arctic structures. To determine the ice force resulting from floe structure interaction, knowledge of the hydrodynamic response due to a moving ice floe is essential.
Two types of hydrodynamic responses to a prescribed ice floe movement are of particular interest:the hydrodynamic frequency response to a periodic motion of an ice floe, andthe hydrodynamic unit function response to an instantaneous change of the floe velocity.
The hydrodynamic frequency response gives rise to the so-called "added mass" and "damping" for an ice floe. The added-mass term represents the hydrodynamic force component that is proportiona1 to the floe acceleration; and the damping term represents that proportional to the floe velocity. Many solution methods are available in the literature to compute the added-mass and damping terms for large floating objects. For example, the two-dimensional problem has been treated using a complex potential representation by Yu and Ursell [1], Kim [2] and Vugts [3], for various shapes including a semi-immersed circular section and different ship-like sections; and has been treated using the finite element method by Bai and Young [4], Newton [5], and Bai [6]. For three dimensional floating bodies of general shape, a numerical scheme has been developed by Garrison [7, 8] for the computation of the added-mass and damping terms based on the source distribution method. However, most existing techniques require complicated numerical procedures that are not well suited for three-dimensional ice floe problem which usually involves very large horizontal dimensions and shallow water depths.
The hydrodynamic unit function response, on the other hand, gives a measure of the hydrodynamic force that would act on an ice floe and hence determines the subsequent motion of the ice floe after its impact with a rigid structure. However, this type of information has seldom been found in the literature. In this paper, a simplified approach will be presented to determine (1) the added mass and damping for a circular I ce floe having two translational (surge and heave) and one rotational (pitch) movements in shallow water.