Energy Dissipation in Viscous-Plastic Sea-Ice Models

In viscous-plastic (VP) sea-ice models, small deformations are approximated by irreversible viscous deformations, introducing a nonphysical energy sink. As the spatial resolution and the degree of numerical convergence of the models increase, linear kinematic features (LKFs) are better resolved and more states of stress lie in the viscous regime. Energy dissipation in this nonphysical viscous regime therefore increases. We derive a complete kinetic energy (KE) balance for sea ice, including plastic and viscous energy sinks to study energy dissipation. The main KE balance is between the energy input by the wind and the dissipation by the water drag and the internal stresses (dissipating 87% and 13% of the energy input on an annual average). The internal stress term is mostly important in winter when ice-ice interactions are dominant. The energy input that is not dissipated locally is redistributed laterally by the internal stresses into regions of dissipation by small-scale deformations (LKFs). Of the 13% dissipated annually by the internal stress term, 93% is dissipated in plastic friction along LKFs (14% in ridging, 79% in shearing) and 7% is stored as potential energy in ridges. For all time and spatial scales tested, the frictional viscous dissipation is negligible in the KE balance. This conclusion remains valid regardless of the degree of numerical convergence of the simulations. Overall, the results confirm the applicability, from an energetical point of view, of the VP approximation.