Three-dimensional surges and recoveries in a numerical glacier model
The Navier–Stokes equation, integrated vertically to yield a two-dimensional transport equation, is combined with the three-dimensional continuity equation. By assuming a linear relation between volume transport and bottom shear stress, a system of numerically tractable differential equations is developed that contains a nonlinear surface slope term and a term in which horizontal frictional forces are stated explicitly. These equations, which are not based on perturbation analysis, are integrated directly on a high speed digital computer. The coefficient of each term in the flow equations is composed of physical parameters (gravity, density, viscosity); therefore, since no quantities such as ice velocities enter the equations, it is only necessary to specify an arbitrary bed configuration and a net-balance versus altitude curve to obtain a glacier solution.For two beds, valley and cirque, steady-state glacier solutions are found for a variety of bed and lateral frictional values. By reducing the bed frict...