ON SHEAR-FLOW OF A SATURATED ICE-SEDIMENT MIXTURE WITH THERMODYNAMIC-EQUILIBRIUM PRESSURE AND MOMENTUM EXCHANGE

Gravity-driven Stokes flow of an ice layer sitting above a layer of ic e mixed with sediments down an inclined plane is considered. The ice i n the top layer and the ice and sediment constituents in the bottom la yer are treated as density-preserving non-Newtonian fluids and their i nterface is treated as fixed. The constitutive relations of the consti tuent stresses and interaction force (between ice and sediment) are ad ditively composed of thermodynamic equilibrium and non-equilibilium co ntributions of which the former are given by a thermodynamic potential , the mixture inner free energy, whose form is motivated by the isotro pic finite strain theory. In the thin-layer approximation, the lowest order governing equations emerge as the limiting equations, valid when the shallowness parameter becomes infinitely small. In this context t he non-dimensionalized momentum balances allow determination of the ac ross-flow variations of the volume fraction of the sediments and mixtu re pressure, independent of those of the streamwise constituent veloci ties. The qualitative agreement of these profiles with corresponding i nformation from observations at the basal layer of glaciers and ice sh eets gives reason for optimism of such a theoretical formulation.