Theoretical analysis of stress perturbations from a partially-lubricated viscous gravity current

Motivated by the flow of grounded ice sheets over meltwater injections at the ice-bed interface allowing the ice to slide and locally accelerate, we analyze the stress perturbations which arise in response to spatially-finite lubrication (slippery patches) beneath a viscous gravity current. We use a reduced-order model to analyze the boundary layer structure of the stress perturbations near the transitions from a no-slip bed to the lubricated slippery patch. The reduced-order model yields a simple analytical result that the amplitude of the perturbation scales linearly with the surface slope and patch length while the decay length scale scales linearly with ice thickness, both of which are measurable quantities. We validated these scalings against 2D along-flow numerical simulations. Through this idealized model, we are able to show relationships between geometry and stress structure which have implications for the Greenland Ice Sheet as the coming decades are projected to see increased injections of lubricating meltwater to the ice-bed interface.