Wave Attenuation in Ice
Authors: Rao G.L. , Vandiver J.K. 
Published: October 2008

ABSTRACT
A theoretical model is presented for the calculation or the attenuation of ocean waves as they pass through partial ice cover. Open water waves, described by a wave spectrum, are assumed to encounter a region of partial ice cover. The method produces a prediction of the attenuated wave spectrum after passage through a user selected distance from the ice edge. The primary mechanism is shown to be wave scattering by individual ice floes.
The theoretical predictive model is compared to results obtained in towing tank studies. The method accounts for flow size, thickness, concentration and distance from the ice edge, and is very simple to implement.

INTRODUCTION
There are locations in the lower Arctic where it may be feasible to use steel space frame structures in 600 to 800 ft. of water. In these regions the environmental loads result from first year ice combined with wind, waves, and current. The conditions may vary from very large waves at times of no ice, to total ice cover and no waves. With these widely varying design conditions the prediction of dynamic response and consequently fatigue life is an imposing task.
A general procedure is presented in Rao (1986) for the estimation of fatigue stresses on a deepwater structure in the Arctic. Information available in current literature was organized within the framework of this general procedure and better methods were developed in some of the weaker areas. In the course of developing an environmental model which adequately represented both waves and ice, an ice-wave interaction model was found to be necessary.
Wave information for the region of interest in the Arctic is usually determined by hind casting techniques. These techniques do not account for the presence of ice. Consequently the local wave environment around a structure may be significantly different from the hind cast one. The model presented here provides a means for estimating the waves in the Vicinity of the structure when there is an ice cover present by accounting for the attenuation of waves by ice.

CURRENT LITERATURE
Apart from the publications of one group of investigators from the Scott Polar Research Institute, Cambridge, there is almost no information in the existing literature on the phenomenon of wave attenuation due to ice. The earliest work on wave attenuation was by Wad hams (1973a). In it an attempt was made to correlate field measurements of attenuation with the results of a very simple theoretical model of one-dimensional backscattering. The model was subsequently developed further in Wad hams (1978).
Although this was followed by a number of field measurement programs, Squire and Moore (1980), Squire and Wad hams (1985), only limited effort was made to relate the results with theoretical models of the kind developed in this research. Wave attenuation in pack ice was also observed by Wad hams (1971) and Squire (1984a). The field data consisted of measurements of wave amplitudes as they penetrated the ice edge.
Based on these measurements an exponential form for the attenuation was proposed, with the exponent being a function of the wave length of the waves