PICS Colloquium: “Kinetic theory for superparameterization of sea ice dynamics”

Arctic sea ice comprises of many ice floes whose dynamics is driven by oceanic/atmospheric currents and floe-floe interaction. Models of the effective sea ice dynamics  at large scales typically employ hydrodynamic equations of motion, such as mass and momentum conservation, with complex constitutive laws attempting to capture the rheology of sea ice as a continuum. Although hydrodynamic sea ice models have enjoyed some successes, they have well-documented limitations in capturing phenomena such as fracture and lead formation, which are direct manifestation of the granular nature of sea ice.

In this talk, we describe a framework that generalizes hydrodynamic models for sea ice using a mesoscopic (kinetic) description that systematically couples macro-scale PDEs with small-scale particle methods. This framework employs a time-dependent probability distribution over floe position and velocity, evolving according to the Boltzmann equation. The mass density and momentum (computed by integrating over the velocity coordinate) evolve according to the same macro-scale hydrodynamic equations used in previous models. However, rather than requiring an effective rheology, kinetic models of the collisions between co-located ice particles determine the small-scale evolution of the conditional density and influence the macro-scale dynamics. To simulate this system efficiently, we construct a two-tiered numerical method that employs finite element methods to solve the macro-scale PDEs and a particle method to evolve the conditional density over the velocity coordinate. We illustrate the framework with idealized numerical experiments demonstrating that it can naturally reproduce phenomena such as ice breakup under a divergent flow.