Continuum mechanical modelling of the dissipative processes in the sediment-water layer below glaciers

The solid mass of the saturated viscous, heat-conducting sediment-water layer below temperate glaciers grows by abrading the underlying rockbed. We propose to model this layer as a saturated mixture continuum of fluid and solid. We formulate its balance laws in volume and jump local forms following, e.g. Germain and Muller (1986). The water balance accounts for its drainage into the rockbed and the melting of ice within the overlaid ice sheet. Dissipation due to the power expended by stresses, the Darcy interaction force and sliding friction governs this thermomechanical system. Our analysis establishes that, contrary to what is stated in the literature, the listed dissipative mechanisms are all relevant.