Spontaneous generation of pure ice streams via flow instability: Role of longitudinal shear stresses and subglacial till

A significant portion of the ice discharge in ice sheets is drained through ice streams, with subglacial sediment (till) acting as a lubricant. The known importance of horizontal friction in shear margins to ice stream dynamics suggests a critical role of longitudinal stresses. The effects of subglacial till and longitudinal stresses on the stability of an ice sheet flow are studied by linear stability analysis of an idealized ice-till model in two horizontal dimensions. A power law-viscous constitutive relation is used, explicitly including longitudinal shear stresses. The till, which has compressible viscous theology, affects the ice flow through bottom friction. We examine the possibility that pure ice streams develop via a spontaneous instability of ice flow. We demonstrate that this model can be made intrinsically unstable for a seemingly relevant range of parameters and that the wavelengths and growth rates that correspond to the most unstable modes are in rough agreement with observed pure ice streams. Instabilities occur owing to basal friction and meltwater production at the ice-till interface. The most unstable wavelength arise because of selective dissipation of both short and long perturbation scales. Longitudinal stress gradients stabilize short transverse wavelengths, while Nye diffusion stabilizes long transverse wavelengths. The selection of an intermediate unstable wavelength occurs, however, only for certain parameter and perturbation structure choices. These results do not change qualitatively for a Newtonian ice flow law, indicating no significant role to shear thinning, although this may very well be due to the restrictive assumptions of the model and analysis.