T. Wu et al., ON SHEAR-FLOW OF A SATURATED ICE-SEDIMENT MIXTURE WITH THERMODYNAMIC-EQUILIBRIUM PRESSURE AND MOMENTUM EXCHANGE, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 454(1968), 1998, pp. 71-88
Citations number
30
Categorie Soggetti
Multidisciplinary Sciences
Journal title
Proceedings - Royal Society. Mathematical, physical and engineering sciences
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.