Ice flow at low deviatoric stress

Abstract

The effective viscosity of ice depends upon many factors, including temperature, deviatoric stress, crystal orientation and impurities. A flow law that includes these factors and is simple to implement is a requirement for numerically efficient ice-flow models. The dominant microscale flow mechanism changes as temperature, deviatoric stress or grain-size changes. For both anisotropic and isotropic constitutive relations, this shift in dominant flow mechanism is expressed as a change in the stress exponent. We study the effects of this shift in stress exponent on ice flow using a two-term flow law for isotropic ice. Our stress-strain-rate relationship does not explicitly describe the microscale processes of ice deformation; however, it encompasses a range of deformation behaviors with a simple law. In terrestrial ice, a flow-mechanism shift may occur in low-deviatoric-stress regions near ice divides, resulting in a near-linear constitutive relationship for ice flow. Compared to a nonlinear (Glen) divide, a divide dominated by a near-linear flow mechanism has vertical-velocity profiles that are similar at divide and flank sites, internal layers that do not develop a Raymond bump, and a steady-state surface profile that is more rounded near the divide.