Deformation in the Vicinity of Ice Divides

Abstract

ABSTRACT. Numerical calculations by finite elements show that the variation of horizontal velocity with depth in the vicinity of a symmetric, isothermal, non-slipping ice ridge deforming on a flat bed is approximately consistent with prediction from laminar flow theory except in a zone within about four ice thicknesses of the divide. Within this near-divide zone horizontal shear strain-rate is less concentrated near the bottom and downward velocity is less rapid in comparison to the flanks. The profiles over depth of horizontal and vertical velocity approach being linear and parabolic respectively. Calculations for various surface elevation profiles show these velocity profile shapes are insensitive to the ice-sheet geometry. RESUME. Deformation au voisinage des difJluences glaciaires. Des calculs numeriques aux elements finis montrent que la variation de la vitesse horizontale avec le profondeur au voisinage d'une diflluence de glace symetrique isotherme et sans glissement sur un lit plat est a peu pres coherente avec les previsions de la theorie de I'eco ulement laminaire sauf dans une zone i:loignee de la diffluence de moins de quatre fois I'epaisseur de la glace. A I'interieur de ceUe zone la deformation visqueuse horizontale est moins concentree vers le fond et la vitesse vers le bas est moin s rapide que vers les rives. Les profils selon la profondeur des vitesses horizontales et verticales sont approximativement I'une lineaire, I'autre parabolique. Les calculs pour differents profils d' altitude superficielle montrent que les formes des profils de vitesse sont independants de la forme geometrique de I'appareil glaciaire.

The Potential for Basal Melting Under Summit, Greenland

“…This must influence the velocity pattern, particularly near the bed where the temperature may at times approach the pressure melting-point. Figure 4, curves A and B, shows that changing from the velocity pattern for isothermal ice (Raymond, 1983) to a pattern calculated for cold ice at Summit changes calculated basal temperatures by about 2.5°C. If velocity and temperature were fully coupled and mutually consistent at each time step, calculated basal temperature would be altered in a complicated way, but by an amount less than 2.5 0c.…”

“…The resu lts for conditions at the divide can be see n in Figure 4. Curve A shows the basal ice temperature over the las t glacial cycle for an ice divide with a flow pattern in Equation (I) for isothermal ice (Raymond, 1983) and with ice conductivity and diffusivity fixed at their O°C values. Curve B shows the basal temperature using the vertical velocity pattern from the central column of nodes in Figure 3 in our two-dimensional velocity model.…”

“…In Figure 4, curve C, we allowed the ice conductivity and ( Raymond, 1983) We overcame the non-linearity this introduced by Newton-Raphson iteration at each time step. The temperatures relative to curve B result from conductivity at low temperatures.…”

“…We first examine some steady models to show that melting is possible. We assume that the vertical velocity pattern v(y) at a steady ice divide can be approximated by (Raymond, 1983) v(y) (I) where y is the height above the bed, H is the ice-sheet thickness , and Vs is the vertical velocity at the surface (equal and opposite to accumulation). Then we solve the steady heat equation o…”

Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique

“…During the past decade several authors have used the finite-element technique to model numerically the flow of an ice mass; Nguyen (unpublished), Schmidt (1977), Iken (1977Iken ( , 1981, Hooke and others (1979), Emery and others (1979), Thomas (1982, 1984), Sikonia (1982), Fastook and Schmidt (1982), Echelmeyer (1983), and Raymond (1983) . Applications have ranged from the overall motion of the Ross Ice Shelf (MacAyeal and Thomas, 1982Thomas, , 1984 to the development of a crack near an ice cliff (Iken,350 Le South Cascade Glacier, Washington, est actuellement en equilibre.…”