A multilayer model for ice flow
Résumé
A new hybrid model for the dynamics of glaciers, ice sheets and ice shelves is introduced. In this model ''multilayer'' the domain of ice consists of a pile of thin layers, which can spread out, tighten and slide over each other. The multilayer model accounts for the two most relevant types of stress: the membrane ones and the vertical shear ones. Assuming the velocity field to be vertically constant on each layer with possible discontinuities between the layers, the model derives from local depth-integrations of the hydrostatic approximation of the Stokes equations. These integrations give rise to interlayer tangential stresses, which are simplified by keeping the vertical shear components of the stress in the local frame of the interface. By imposing continuity of the stress between layers, the final model consists of a system of two-dimensional non-linear elliptic equations, the size of this system equal to the number of layers. By construction, the model is a multilayer generalisation of the Shallow Shelf Approximation (SSA), which corresponds to the 1-layer model. Like the SSA, the multilayer model can be advantageously reformulated as a minimisation problem. Numerical techniques developed for the SSA can be used, provided an iterative loops over the layers. The multilayer model is used to compute the two-dimensional velocity fields of two benchmark experiments. Although it is mathematically two-dimensional, the multilayer model shows good agreement with the three-dimensional higher-order models on these experiments.
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