Tidewater glaciers and large ice sheets, e.g. the Antarctic ice sheet and a late-Würm Arctic ice sheet, are complex but single dynamic systems composed of terrestrial, marine and floating parts. Morphology and dynamics of the different parts are different. The terrestrial parts are convex and their dynamics are controlled by shear stress only (the longitudinal stress is zero); the floating parts are concave and their dynamics are controlled by longitudinal stress only (the shear stress is zero). To connect the different parts we should consider transitional zones where shear and longitudinal stresses are comparable.

To describe glacier and ice-sheet dynamics, longwave approximation of the first order is used. In this approximation it is impossible to connect terrestrial and floating parts dynamically, only morphologically and kinematically. It means that the first-order longwave approximation is not sufficient.

If the transitional zone between the terrestrial and floating parts is long in comparison to ice thickness (in hydrodynamics the term “weak” is used) we can do the next step in the longwave approximation to describe the single dynamical system consisting of the terrestrial and floating parts and the weak transitional zones (ice streams). It is a purely hydrodynamical approach to the problem without ad hoc hypothesis.

The presented model is a non-stationary three-dimensional hydrodynamic model of glaciers and ice sheets interacted with ocean, involving the conditions of ice continuity and dynamic equilibrium, ice rheology, and boundary conditions on the free surface (dynamic and kinematic) and on the bed (ice freezing or sliding). Longwave approximation is used to reduce the three-dimensional model to a two-dimensional one. The latter consists of (1) evolution equations for grounded and floating parts and weak transitional zones; (2) boundary conditions on the fronts (e.g. the conditions of calving); (3) equations governing the junctions of the parts (the most important junction is the grounded line) with the conditions connecting the evolution equations.