K. Hutter et al., ON INTERFACIAL TRANSITION CONDITIONS IN 2 PHASE GRAVITY FLOW, Zeitschrift fur angewandte Mathematik und Physik, 45(5), 1994, pp. 746-762
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.