Modelling capsizing icebergs in the open ocean

At near-grounded glacier termini, calving can lead to the capsize of kilometre-scale (i.e. gigatons) unstable icebergs. The transient contact force applied by the capsizing iceberg on the glacier front generates seismic waves that propagate over teleseismic distances. The inversion of this seismic signal is of great interest to get insight into actual and past capsize dynamics. However, the iceberg size, which is of interest for geophysical and climatic studies, cannot be recovered from the seismic amplitude alone. This is because the capsize is a complex process involving interactions between the iceberg, the glacier and the surrounding water. This paper presents a first step towards the construction of a complete model, and is focused on the capsize in the open ocean without glacier front nor ice-mélange. The capsize dynamics of an iceberg in the open ocean is captured by computational fluid dynamics (CFD) simulations, which allows assessing the complexity of the fluid motion around a capsizing iceberg and how far the ocean is affected by iceberg rotation. Expressing the results in terms of appropriate dimensionless variables, we show that laboratory scale and field scale capsizes can be directly compared. The capsize dynamics is found to be highly sensitive to the iceberg aspect ratio and to the water and ice densities. However, dealing at the same time with the fluid dynamics and the contact between the iceberg and the deformable glacier front requires highly complex coupling that often goes beyond actual capabilities of fluid-structure interaction softwares. Therefore, we developed a semi-analytical simplified fluid-structure model (SAFIM) that can be implemented in solid mechanics computations dealing with contact dynamics of deformable solids. This model accounts for hydrodynamic forces through calibrated drag and added-mass effects, and is calibrated against the reference CFD simulations. We show that SAFIM significantly improves the accuracy of the iceberg motion compared with existing simplified models. Various types of drag forces are discussed. The one that provides the best results is an integrated pressure-drag proportional to the square of the normal local velocity at the iceberg's surface, with the drag coefficient depending linearly on the iceberg's aspect ratio. A new formulation based on simplified added-masses or computed added-mass proposed in the literature, is also discussed. We study in particular the change of hydrodynamic-induced forces and moments acting on the capsizing iceberg. The error of the simulated horizontal force ranges between 5 and 25 per cent for different aspect ratios. The added-masses affect the initiation period of the capsize, the duration of the whole capsize being better simulated when added-masses are accounted for. The drag force mainly affects the amplitude of the fluid forces and this amplitude is best predicted without added-masses.