ABSTRACT
The force that makes ice flow in the direction of decreasing surface elevation is the driving stress as defined in equation (3.21). This action is opposed by reactions, or resistive forces. Resistance to flow may originate at the glacier bed and at the lateral margins, or resistance may be associated with gradients in longitudinal stress (c.f. Section 3.1). Generally, because of the nonlinearity of the flow law, a velocity solution cannot be derived analytically, except in simplified cases where flow resistance is offered by only one of these potential sources. While this may appear overly restrictive, these limiting cases do apply to certain flow regimes found in Nature. Flow in the interior of ice sheets is mostly controlled by a balance between driving stress and drag at the glacier bed, and the corresponding lamellar flow model provides a good approximation of ice flow. On mountain glaciers, lateral drag arising from friction between the ice and valley walls may provide resistance to flow in addition to basal drag. In first approximation, this effect can be incorporated by introducing a shape factor to reduce basal drag in accordance with the role of lateral drag, but otherwise adopting the lamellar flow model. On Whillans Ice Stream in West Antarctica, basal friction is vanishingly small due to the presence of a water-saturated weak layer of sediment (for example, Whillans and van der Veen, 1997) and the driving stress is balanced almost entirely by lateral drag originating at the margins where the ice stream moves past nearly stagnant ice (van der Veen et al., 2007). This model of flow controlled by lateral drag also applies to floating ice shelves in comparatively narrow fjords. Finally, on free-floating ice shelves, the only resistance to flow is associated with gradients in longitudinal stress. In this chapter, these “end member” solutions are discussed.
