Cylindrical Flow in and Over Channels of Irregular Shape

Abstract

ABSTRACT. Earlier work by Nye (1965), who obtained numerical solutions for axial independent flow of a non-linear Glen material in channels of rectangular, elliptic, and parabolic cross-sections with a nUll-slip basal condition, is extended by using an inverse technique. Exact analytical solutions are obtained for flow in irregular-shaped channels (subject to symmetry restrictions) for both a Newtonian and an n = 3 Glen material. The cross-sections are regulated by multi-parameters. Solutions are obtained for two types of channel: (a) those whose side walls meet the free ice surface vertically, and (b) periodic channel arrays whose basal profiles do not intersect the free ice surface, i.e. overfilled channels.Solutions for the second type have not been presented previously. The solutions for the 11 = 3 Glen material employ a small parameter which limits the geometry vanatlOn to perturbations on semicircular or uniform-depth channels. Basal slip conditions can be incorporated although results are not presented here.

Parameterization of lateral drag in flowline models of glacier dynamics

“…Ice velocities in and over a valley cross section have been discussed several times before in rectangular and parabolic channels (e.g. Nye, 1965;Shoemaker, 1985). Here we give attention to the respective variations in cases with slipinduced lateral drag.…”

“…Proper parameterization of slip-induced lateral drag is therefore necessary to enhance the dynamical realism of flowline models. Previous workers have analyzed the flow in channels of irregular cross sections (Shoemaker, 1985) and assessed the effects of basal sliding on valley glacier dynamics (e.g. Reynaud, 1973;Harbor, 1992), but none of them present parameterizations or guidance for flowline models.…”