On the distribution of stress and velocity in an ice strip, which is partly sliding over and partly adhering to its bed, by using a Newtonian viscous approximation

Abstract

An infinitely long strip of a Newtonian fluid held between two parallel planes subjected to gravity is regarded as a reasonable model to investigate the stress concentration and the velocity distribution occurring near boundary points where perfect-slip goes over into no-slip. By using the Wiener-Hopf technique a stress singularity of order x 1/2 is derived at the no-slip-perfect-slip junction, and the velocity transition from uniform flow far upstream to Poiseuille flow far downstream is deduced. It is shown that the maximum surface velocities are nearly twice as large as those occurring in Poiseuille flow and it is argued that the stress singularities could account for the high gravel concentration frequently found near the bottom of ice boreholes. Numerical results of the analytical stress and velocity representations are presented, and the limitations of the present theory are discussed.