Calculating cumulative strain

In order to calculate the cumulative strain in a glacier, one first must know the velocity field. One then calculates the path that a particle of ice would follow through the glacier and velocity derivatives at discrete points along the path. To obtain the incremental strain as the ice moves from one point to the next, strain rates are then calculated from the velocity derivatives and multiplied by the time needed for this movement (b) Direction of maximum cumulative extension Figure 13.5. (a)...

Conduction

The energy content of the control volume may also change as a result of conduction of heat. Consider the situation depicted in Figure 6.2 in which the temperature gradient across the left-hand face, dy dz, is d0 dx, and that across the corresponding right-hand face is The heat flux is proportional to the temperature gradient. The constant of proportionality is K, the thermal conductivity of ice. Thus, on the left-hand face there is a heat flux Heat flows from warm areas to cold areas, which...

Submergence and emergence velocities

Earlier (Equation (5.1)), we gained insight into the magnitude of the horizontal velocity by considering a glacier in a steady state, such that its surface profile remained unchanged. Let us now use this idealization to study vertical velocities. In such a steady state, the surface in the accumulation area must everywhere be sinking at a rate that balances accumulation, and conversely in the ablation area. Thus, the vertical velocity at the surface, ws, is clearly related to the net balance...

Why study glaciers

Before delving into the mathematical intricacies with which much of this book is concerned, one might well ask why we are pursuing this topic - glacier mechanics For many who would like to understand how glaciers move, how they sculpt the landscape, how they respond to climatic change, mathematics does not come easily. I assure you that all of us have to think carefully about the meaning of the expressions that seem so simple to write out but so difficult to understand. Only then do they become...

Summary

We began this chapter by deriving the energy balance equation. Given boundary conditions appropriate for a polar ice sheet, solutions to this equation yield the temperature distribution in the ice sheet. The boundary conditions most commonly used are (1) the temperature at the surface, which is approximated by the mean annual temperature, perhaps with a correction for heating by percolating melt water and (2) the temperature gradient at the bed. The latter is based on estimates of the...

Deformation of subglacial till

We have known for decades that ice moving over granular subglacial materials can deform these materials. (Herein, the term granular material should be understood to include materials with significant amounts of clay, although a distinction between granular materials and clays is usually made in the soil mechanics literature.) Commonly, the granular material is till, either formed by erosion during the present glacial cycle, or left from a previous one. Recently it has become clear that a large...

The upper part of the englacial hydraulic system

Veins and the initial development of passages Nye and Frank (1973) argued that veins should be present along boundaries where three ice crystals meet, and that at four-grain intersections these veins should join to form a network of capillary-sized tubes through which water can move. They thus concluded that temperate ice should be permeable. Such capillary passages have been observed in ice cores obtained from depths of up to 60 m on Blue Glacier, Washington (Figure 8.1a) (Raymond and...