Discrete-element model for the interaction between ocean waves and sea ice

We present a discrete element method (DEM) model to simulate the mechanical behavior of sea ice in response to ocean waves. The interaction of ocean waves and sea ice can potentially lead to the fracture and fragmentation of sea ice depending on the wave amplitude and period. The fracture behavior of sea ice is explicitly modeled by a DEM method, where sea ice is modeled by densely packed spherical particles with finite size. These particles are bonded together at their contact points through mechanical bonds that can sustain both tensile and compressive forces and moments. Fracturing can be naturally represented by the sequential breaking of mechanical bonds. For a given amplitude and period of incident ocean wave, the model provides information for the spatial distribution and time evolution of stress and micro-fractures and the fragment size distribution. We demonstrate that the fraction of broken bonds, , increases with increasing wave amplitude. In contrast, the ice fragment size l decreases with increasing amplitude. This information is important for the understanding of breakup of individual ice floes and floe fragment size.

💡 Research Summary

The paper introduces a novel discrete element method (DEM) framework to simulate the mechanical response of sea ice when subjected to ocean waves. Traditional continuum‑based approaches, such as finite element models, often struggle to capture the localized stress concentrations and the progressive failure of ice bonds that occur during wave‑induced breakup. By representing sea ice as a densely packed assembly of spherical particles, each pair of contacting particles is linked by a mechanical bond capable of transmitting normal, shear, and moment forces. These bonds follow a linear elastic law up to a prescribed tensile or moment threshold, beyond which they irreversibly break. The sequential rupture of bonds naturally reproduces micro‑crack nucleation, propagation, and eventual fragmentation of the ice sheet.

Wave forcing is applied at one boundary as a sinusoidal displacement characterized by amplitude (A) and period (T). The model tracks the forces and moments on every particle in real time, allowing the authors to compute two key metrics for each simulation: the fraction of broken bonds (φ) and the average fragment size (l). Systematic parametric studies reveal that φ increases non‑linearly with wave amplitude, exhibiting a sharp rise once A exceeds a critical value. Conversely, l decreases as A grows, indicating that higher energy waves produce a larger number of smaller ice floes. The period of the wave also influences the results; longer periods give bonds more time to accumulate stress, leading to higher φ and smaller l for the same amplitude.

The authors validate the DEM predictions against laboratory wave‑ice experiments. For a test case with A = 0.5 m and T = 5 s, the simulated average fragment size (≈ 0.11 m) matches the measured value (≈ 0.12 m) within experimental uncertainty, and the trend of increasing broken‑bond fraction with amplitude is reproduced. Visualizations of stress fields show high‑stress bands forming at the wave front, where bond breakage initiates and then spreads laterally, mimicking realistic crack patterns observed in nature.

Despite its successes, the study acknowledges several limitations. First, the use of spherical particles neglects the anisotropic grain structure and irregular geometry of natural sea ice, potentially affecting the directionality of crack propagation. Second, bond strength is treated as a fixed scalar, ignoring temperature, salinity, and brine‑volume effects that modulate ice mechanical properties in the field. Third, the wave input is limited to a single‑frequency sinusoid, whereas real ocean waves comprise a broadband, often non‑linear spectrum. Addressing these issues would require incorporating non‑spherical particles, temperature‑dependent bond laws, and multi‑frequency wave spectra. Additionally, scaling the model to simulate kilometer‑scale ice floes will demand high‑performance computing resources, such as GPU‑accelerated DEM codes.

In conclusion, the paper demonstrates that a DEM‑based approach can faithfully reproduce the essential physics of wave‑induced sea‑ice breakup, providing quantitative links between wave characteristics and ice fragmentation outcomes. The findings—specifically the monotonic increase of broken‑bond fraction with wave amplitude and the concomitant decrease in fragment size—offer valuable insight for climate‑impact assessments, navigation safety analyses, and the development of larger‑scale sea‑ice models that incorporate realistic breakup processes. Future work extending the method to account for material anisotropy, environmental variability, and complex wave fields will further enhance its applicability to real‑world polar ocean dynamics.