The Flow of Ice, Treated as a Newtonian Viscous Liquid, around a Cylindrical Obstacle Near the Bed of a Glacier

Abstract

This paper describes an analytical solution of the equations of motion and heat conduction for ice flowing around a cylindrical solid inclusion and over a solid plane boundary. This is intended to be a simplified representation of the flow of clean glacier ice around a stone and over a rigid rock bed. The ice is treated as a Newtonian viscous liquid and the equations are solved in two dimensions. Regelation boundary conditions are applied at both ice–rock interfaces. It is found that finite solutions for the temperature and stream function only exist for the special cases in which two dimensionless critical wavelengths are zero. That is, unless the stone is very far from the glacial bed, the classical regelation boundary conditions cannot be obeyed over the whole of its surface.