Application of Discrete Element Methods to Approximate Sea Ice Dynamics

Abstract

Lagrangian models of sea ice dynamics have several advantages over Eulerian continuum models. Spatial discretization on the ice floe scale is natural for Lagrangian models and offers exact solutions for mechanical nonlinearities with arbitrary sea ice concentrations. This allows for improved model performance in ice-marginal zones, where sea ice is fragmented. Furthermore, Lagrangian models can explicitly simulate jamming processes that occur when sea ice moves through narrow confinements. While difficult to parameterize in continuum formulations, jamming emerges spontaneously in dense granular systems simulated in a Lagrangian framework. Here we present a flexible discrete element framework for approximating Lagrangian sea ice mechanics at the ice floe scale, forced by ocean and atmosphere velocity fields. Our goal is to evaluate the potential of models simpler than the traditional discrete element methods for granular dynamics. We demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to produce jamming and describe two different approaches based on Coulomb friction and cohesion which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model displays jamming behavior which is similar to the more complex model with Coulomb friction and ice floe rotation at larger scales and has significantly lower computational cost.

The Effects of Ice Floe‐Floe Interactions on Pressure Ridging in Sea Ice

“…We model the sea-ice mechanics with a Lagrangian formulation based on the discrete-element method with breakable bonds (e.g., Cundall & Strack, 1979;Potyondy & Cundall, 2004;Herman, 2016;Damsgaard et al, 2018). The model is two-dimensional, with a horizontal (x) and a vertical axis (z).…”

“…4 Ridging Parameterization for Large-scale Simulations Large-scale particle sea-ice models have the potential to improve simulation of the marginal ice zone and other places where granular mechanics dominate the deformation (e.g., Gutfraind & Savage, 1997;Hopkins, 2004;Feltham, 2005;Herman, 2016Herman, , 2017Damsgaard et al, 2018). On this scale, each particle typically represents a single ice floe, but a physically-motivated ridging scheme is missing.…”

“…The study of ice strength is motivated not only by the perspective of sea-ice modeling, but also from the need to understand ice clogging of rivers, lakes, and marine passages (e.g., Shen & Liu, 2003;Herman, 2013;Rallabandi et al, 2017;Damsgaard et al, 2018), and mechanical resistance and wear against ships and other artificial structures (e.g., Timco et al, 2000;Heinonen, 2004). Coulomb failure is a general and scale-independent measure of ice strength (e.g., Weiss & Schulson, 2009), and has served as the constitutive basis for a range of mechanical analyses.…”

The effects of ice floe-floe interactions on pressure ridging in sea ice

“…We model the sea-ice mechanics with a Lagrangian formulation based on the discrete-element method with breakable bonds (e.g., Cundall & Strack, 1979;Damsgaard et al, 2018;Potyondy & Cundall, 2004;Herman, 2016). The model is two-dimensional, with a horizontal (x) and a vertical axis (z).…”

Comment on tc-2020-354

“…While several improvements were made on the numerics and efficiency of the methods used to solve the highly non-linear momentum equation (Hunke, 2001;Lemieux et al, 2008Lemieux et al, , 2014Kimmritz et al, 2016;Koldunov et al, 2019), the physics governing the ice fracture remains mostly the same. A number of rheologies have however been developed over the years in an attempt to simulate the observed sea-ice deformations (Tremblay and Mysak, 1997;Wilchinsky and Feltham, 2004;Schreyer et al, 2006;Sulsky and Peterson, 2011;Rampal et al, 2016;Dansereau et al, 2016;Damsgaard et al, 2018). Among these new approaches, a damage parameterization derived for rock mechanics and seismology models (Amitrano et al, 1999;Amitrano and Helmstetter, 2006) was adapted for the large scale modelling of sea ice (Girard et al, 2011;Bouillon and Rampal, 2015).…”