where é¡j is the strain-rate tensor, t¡¡ is the deviatoric-stress tensor and teff is the second invariant of tj> E is an enhancement factor (with subscripts referring to linear, l, and non-linear, nl, processes); Ao is the temperature-independent part of the softness parameter defined for clean, isotropic Holocene ice; d is grain size (with exponent p); Q is activation energy; and T is temperature. Although this formulation of the flow law does not account for
Glen term each separate mechanism, its form can approximate the behaviour observed by laboratory and field experiments. Equation (1) can also be written eij = F[k + T^ff] Tj where
where k is the crossover stress: the effective deviatoric stress at which the linear and non-linear terms contribute equally to the total strain rate. The variable k is a rheological property of ice; although it may depend on temperature and grain size, it is independent of the geometry and climate of the ice sheet. Prior to this work, the stress at which the dominant flow mechanism changes was poorly known. Here I use conditions at Siple Dome to determine k.
This linear term becomes significant only at low deviatoric stresses. The lowest stresses in an ice sheet are found in the icedivide region, where both normal and shear stresses approach zero. As Raymond (1983) observed, the non-linear nature of Glen's Law predicts very stiff ice under the divide where stresses are low, when compared with ice on the flanks. This stiff ice affects the flow and, therefore, the internal stratigraphy. Raymond predicted that a steady-state divide would reflect this special flow pattern by forming an arch in the isochrons. If a linear flow mechanism dominates at low stress this special divide flow pattern would be altered.
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