Anderson localization of oceanic waves in ice-covered seas

In recent years, there has been an increasing need to incorporate the interaction of oceanic waves with floating sea ice covers in order to significantly improve current Earth/climate models and predictions of seasonal sea ice evolution. In most climate models, simple power and exponential laws are assumed to describe the frequency-dependent wave attenuation that occurs as oceanic waves propagate further into the ice pack. However, it is becoming clear that these simplistic assumptions lack the fidelity to properly capture the vast complexity that actually occurs in Earth’s polar regions. The work presented here combines the mathematics of quantum mechanics with homogenization theory in order to establish broad and applicable relationships between the geometry of sea ice floes and the subsequent attenuation of oceanic waves. This is accomplished by analyzing the spectral statistics of real symmetric, random matrices which govern mechanical wave transport through viscoelastic composite materials. For certain geometric configurations of ice floes, we observe the hallmarks of Anderson localization - the spectral properties produce band gaps, mobility edges, and transitions toward universal statistics of the Gaussian orthogonal ensemble.