Analysis and numerical simulations of a landfast ice model

Abstract

In this manuscript, we consider a common modeling framework for Arctic landfast ice based on the work of Lemieux et al. [27], which is designed for use in large-scale climate models. This approach extends the classical viscous-plastic sea-ice model introduced by Hibler [18], which remains the most widely used model for simulating large-scale sea-ice dynamics. In particular, landfast ice refers to sea-ice that is attached to the coastline or grounded and therefore exhibits nearly vanishing motion. The model considered in this manuscript augments Hibler's viscous-plastic sea-ice model by tensile strength and a threshold-dependent basal stress. We present a rigorous analytical and numerical study of this landfast ice model. The analytical contributions are the local strong well-posedness, the global strong well-posedness in the absence of external forces and for initial data close to constant equilibrium solutions, and the existence of time-periodic solutions. The limiting case $k_{\mathrm{t}} \equiv 1$ is treated separately, since the pressure coupling then vanishes and a new smallness condition on the stress regularization parameter is required. For the system without scalar diffusion, we establish local strong well-posedness through a Lagrangian formulation and anisotropic maximal $\mathrm{L}^p$-regularity. Finally, we perform numerical simulations that illustrate key qualitative differences between landfast ice and classical viscous-plastic sea-ice models. The simulations reveal the formation of stationary equilibrium states characterized by vanishing ice velocity. These observations are consistent with the global-in-time existence result close to equilibria established in Theorem 4.1 and the time-periodic result in Theorem 5.2. The combined analytical and numerical results provide new insight into the structure, stability, and long-term behavior of landfast ice dynamics.