Divide flow and Raymond bumps
We alluded to this a bit earlier in our discussion of higher-order model Basics. Even for very slow flowing areas of an ice sheet - e.g. an ice divide - accounting for horizontal-stress gradients can be important for getting the flow field, and in this case the geometry, right. The odd, angular shape of a flow divide for the case of n=3 is a result of the very low deviatoric stresses there and the non-linearity in the flow law. Because the surface slope at the divide is ~0 there is essentially no vertical shear within the ice column. All of the deformation is due to horizontal stretching. As a result, the effective viscosity of the ice beneath the divide is very high, relative to on either side of the divide where slope and vertical shear are not zero; there is a stiff "spine" of ice at the divide giving it a peaked shape. For a Newtonian-viscous flow, the flow divide is relatively more rounded because this stiff spine is lacking. Note that a shallow-ice model could not predict this behavior, as it lacks the horizontal stresses which dominate underneath the divide.
This same mechanism is behind the phenomenon of "Raymond" bumps (named after Charlie Raymond who predicted their existence from theory (Raymond; 1983) long before they were observed in the field), an arched shape in the internal layers beneath a flow divide. The stiffer ice beneath the divide inhibits the downward flow of ice there and, as a result, layers seen in radio-echo sounding form what appears to be a bump. Another way to look at it is that the vertical velocity profile beneath a divide differs - downward flow is relatively slower - because of the different stress regime there.
Figure 1: Raymond bump at Siple Dome, as observed in radio-echo sounding detected internal layers. Ice Stream D (Bindschalder) is to the right and Ice Stream C (Kamb) is to the left (radar image after Gades and others (2000)).
Figure 2: Internal layers at Siple Dome simulated using a full Stokes flowline model (model described in Price and others (2007)).
Gades, A. M., C. F. Raymond, H. Conway and R. W. Jacobel. 2000. Bed prop-erties of Siple Dome and adjacent ice streams, West Antarctica, inferred from radio-echo sounding measurements. J. Glaciol., 46(152), 88-94.
Price, S.F., E.D. Waddington, and H. Conway. 2007. A full-stress, thermomechanical flowband model using the finite volume method. J. Geophys. Res., 112, F03020, doi:10.1029/2006JF000724.
Raymond, C. (1983), Deformation in the vicinity of divides, J. Glaciol., 34, 357 – 373