Basal sliding

Basal sliding is motion of glacier ice relative to its bed. A sliding law relates the basal velocity to basal shear stress, effective pressure, roughness, or other bed properties.

A linear basal drag law has resisting traction $-\mu \beta u_b$, with $\beta >0$ of dimension inverse length. It idealizes lubrication by subglacial till and is equivalent to a Navier slip boundary condition of slip length $1/\beta$ when the ice is a Newtonian fluid. It is a constitutive idealization, not a universal sliding law.

Subglacial till is a mixture of rock fragments and fine sediment beneath ice. A wet deformable layer can lubricate basal sliding. Its constitutive equation must be specified; Newtonian till lubrication is one idealization, rather than a claim that all subglacial till is a Newtonian fluid.

A thin layer of subglacial till idealized as a Newtonian fluid of dynamic viscosity $\lambda \mu$ and thickness $l$ undergoes Couette flow between stationary bedrock and ice moving at speed $u$. Its resisting basal shear stress has magnitude ${\tau }_b=\lambda \mu u/l$ and acts opposite to the sliding motion. Combining this drag with the hydrostatic driving force gives the bulk approximation used in the friction-dominated grounding-line evolution law.