Particle, kinetic and hydrodynamic models for sea ice floes. Part II: Rotating floes with nonlinear contact forces

TL;DR

This paper advances sea ice floe modeling by incorporating rotational dynamics and nonlinear contact forces, leading to more realistic multiscale descriptions of ice behavior under environmental influences.

Contribution

It generalizes existing particle-kinetic-hydrodynamic models to include rotation and nonlinear contact interactions, enriching the macroscopic equations for sea ice dynamics.

Findings

Inclusion of rotational motion and nonlinear contact forces in the model.

Derivation of extended kinetic and hydrodynamic equations with additional stress terms.

Enhanced realism in simulating sea-ice rheology and response to environmental forces.

Abstract

This paper extends the multiscale modeling framework introduced in Part I (Deng and Ha, Physica D: Nonlinear Phenomena 483 (2025) 134951) for sea-ice floe dynamics with non-rotating floes to the case with rotational floes and nonlinear contact interactions. Building on the particle-kinetic-hydrodynamic hierarchy developed for non-rotating floes, we generalize the particle model to describe ice floes as rigid bodies characterized by position, linear velocity, angular velocity, size, and moment of inertia. The interaction rules now include nonlinear contact forces and torques arising from short-range compression, restitution, and tangential friction laws, together with hydrodynamic drag that couples translational and rotational motions. These particle descriptions lead to an enriched Vlasov-type kinetic equation posed on an extended phase space, whose moments yield a hydrodynamic system for mass, momentum, and angular-momentum balances. Compared with Part I, the resulting macroscopic equations feature additional stress contributions, rotational transport, and dissipative mechanisms stemming from nonlinear collisions. The proposed framework provides a more realistic description of sea-ice floe dynamics and offers a systematic pathway toward multiscale modeling of sea-ice rheology under complex environmental forcing.