ON INTERFACIAL TRANSITION CONDITIONS IN 2 PHASE GRAVITY FLOW

A layer of ice and sediment is modelled as a mixture of two nonlinear, very viscous, constant density fluids interacting mechanically via Da rcy- and Fick-type forces. An inclined layer of this mixture overlain by a layer of ice modelled as a viscous fluid is considered with bound ary conditions of no-slip or viscous sliding at the base and no stress at the free surface. The interface is treated as a singular surface a cross which the jump conditions of mass and momentum for the constitue nts are assumed to hold. Furthermore, because the components are visco us fluids, a kinematic condition for the continuity of the tangential velocity is formulated. The momentum jump conditions involve surface p roduction terms requiring additional surfacial constitutive relations. We show that the posed physical problem admits a mathematical solutio n only in the case that the interface momentum production is non-zero.