A continuum mixture model of ice stream thermomechanics in the Laurentide Ice Sheet .1. Theory

We employ a continuum mixture framework to incorporate ice streams in a three-dimensional thermomechanical model of the Laurentide Ice Sheet. The ice mass is composed of a binary mixture of sheet ice, which deforms by viscous creep, and stream ice, which flows by sliding and/or sediment deformation at the bed. Dynamic and thermal evolutions are solved for each component in the mixture, with coupling rules to govern transfer between flow regimes. We describe two different transfer mechanisms: (1) creep exchange, the nourishment of ice streams by viscous creep inflow from the surrounding ice sheet, and (2) bed exchange, the activation, growth, and deactivation of ice streams, perpetrated by transfers of bed area between flow constituents. This paper develops the underlying mixture theory. We express the governing equations for mass, momentum, and energy balance in a form suitable for direct incorporation in existing numerical models of ice thermomechanics. A companion paper in this issue explores mixture and ice stream behavior in applications with the Laurentide Ice Sheet.