| الوصف: |
The flow of glaciers and ice-sheets is controlled by internal deformation and basal sliding. Daily to seasonal variations in ice flow are mostly the result of changes at the interface between the ice and the bedrock induced by the presence of water. More than six decades ago, Lliboutry (1958) formulated the role of this water in its ability to modulate the friction at the base of glaciers through the opening of water cavities. Since this pioneer work, a number of efforts have been undertaken to formalize mathematically the form of a water-pressure-dependent friction law for glaciers, i.e. the relation that gives the basal shear stress as a function of the sliding velocity, the water pressure and potentially other state variables. If a number of initial assumptions used to derive these friction laws have been overcome recently (e.g. three dimensional geometries, synthetical or realistic, existence of solid friction at the interface ice-bed, validation against datasets), all these recent efforts still assume that the geometry of the cavities instantaneously adapt to any change in water pressure. Whereas this might hold for long term water pressure variations at seasonal scale, this is certainly not true for daily variations during which the cavity geometry cannot adapt sufficiently fast. In this presentation, using the same finite element method framework as in Gagliardini et al. (2007), the effect of non-steady water pressure within the cavity is studied. For daily variations of water pressure, it is shown that the solution strongly departs from the steady-state one, but still instantaneously depends on effective pressure. Following Thøgersen et al. (2019) and Gilbert et al. (submitted), a cavity ratio is introduced as a new state variable in the friction law to account for departure to steady-state geometry. Using different types of perturbation, a transient friction law associated to an evolution equation for the cavity ratio is proposed to reproduce the numerical experiments. This new law can further be useful for a consistent coupling between ice flow and hydrological models where cavity geometry is modeled as a transient process in both models.References:Gagliardini et al. (2007) Finite-Element Modeling of Subglacial Cavities and Related Friction Law. J. of Geophys. Res., Earth Surface, 112.Gilbert et al. (submitted) A Consistent Framework for Coupling Basal Friction with Subglacial Hydrology on Hard-bedded Glaciers, GRL.Lliboutry (1958) Contribution à la théorie du frottement d'un glacier sur son lit. Compte Rendus à l’Académie des Sciences, pp 317-320.Thøgersen et al. (2019) Rate-and-state friction explains glacier surge propagation. Nature Communications, 10(1), 2823. |
