Approximation Of Two-dimensional Flow Research Articles

Asymptotic analysis of flow near a glacier terminus

AbstractThe non-linearly viscous ice flow in the vicinity of a glacier terminus, an observation region, depends crucially on the upstream flow as well as on the local surface and bed conditions. The former requires a likely complex solution of the balance laws and boundary conditions for the complete glacier. However, if the profile and downstream surface tangential velocity in the observation region are measured at an observation time t = 0, and a two-dimensional flow approximation is satisfactory, the complete stress and velocity fields satisfying local reduced model equations in the observation region at time t = 0 can be determined by asymptotic expansions in upstream distance from the (moving) terminus. Thus the full strain-rate and stress tensors are determined without prescribing the basal conditions. The terminus velocity is determined in terms of the net accumulation or melt flux and surface velocity at the terminus, with bounds for advance or retreat. The analysis and illustration are presented for a plane flow approximation.

Numerical and experimental investigation of the gas dynamics of flat symmetric nozzles with a section of constant height and two bends of the profile in the region of the critical section

On the basis of a numerical and experimental investigation the pressure distributions are obtained along the walls of contracting and expanding flat symmetric nozzles having a section of constant, height in the region of the critical section. It is shown that a calculation in the approximation of two-dimensional flow of an ideal gas makes it possible to obtain basically reliable data. The flow is basically determined by the inviscid core of the flow, and the influence of the boundary layers is relatively small and manifested only at points of abrupt change of the pressure. The presence of a contracting part with straight walls and a section of constant height in the critical section gives rise to an appreciable disturbance of the flow at the start of the expanding part of the nozzle, but the disturbances are rapidly damped in the longitudinal direction.