Wave Propagation in a Solid Ice Pack

Abstract

The analysis presented in this paper was inspired by the report that the R/V Polarstern has encountered surface waves of large amplitude hundreds of kilometers inside the ice pack in the Weddell Sea. This paper presents analysis of processes that affect waves in an ice pack, namely the refraction of waves at the pack edge, the effects of pack compression on wave propagation, wave train stability and buckling stability in the ice pack. Sources of pack compression and interaction between wave momentum and pack compression are discussed. Viscous damping of propagating waves are also studied. Significant results include the conditions for total reflection of waves at the pack edge, the strong effect of pack compressive stress on wave group speed, with the concomitant possibility of extreme local concentration of wave energy. The result that compressive stress in the pack leads to very rapid development of wave packets, through changes in the parameters for weakly nonlinear modulational instability of the wave field is also notable. The analysis suggests an explanation for the change in wave dispersion observed from the ship between the time of first arrival of the waves and after the pack was partially broken up by the first waves.