3D Discrete Element Model and Continuum Theory for Granular Flow of Ice Mélange

Ice mélange is a granular pack of sea ice and icebergs that is tightly packed in glacier fjords and can suppress iceberg calving by providing resisting stresses called buttressing. Without measurements of buttressing forces provided by ice mélange, it remains challenging to predict glacial calving events and thus the mass loss of ice sheets.

To quantify the buttressing force, previous work has developed 2D discrete element models (DEM) to model mélange as a 2D floating granular material. However, lab experiments and observations suggest that mélange thickness varies along the flow and deviate from a 2D granular pack. Here we develop the first 3D DEM that simulates a moving terminus pushing against a collection of cubic icebergs confined within a channel. We also examine the effect of realistic fjord geometry of two Greenland tidewater glaciers. The mélange near the glacier terminus moves at the terminus velocity with shear bands developed at fjord walls. The modeled velocity field showcases both uniform and extensional flow regimes that are consistent with remote observations. We developed a 3D continuum theory that resembles shallow shelf approximation to describe the flow of ice mélange. We validated the continuum theory by DEM simulations and found that the driving stress induced by the mélange thickness gradient is predominantly balanced by the fjord friction resisting the granular flow. The resulting analytical model reveals that the buttressing force depends on the square of the mélange thickness, and the thickness decays exponentially from the terminus, exhibiting excellent agreement with 3D DEM simulations. Finally, from remote observations across 32 Greenland glacier termini, we find thick mélange when terminus advances in winter, and thin mélange when terminus retreats in summer, that can be explained by the seasonal varying mélange buttressing force predicted from our models.