Homework #4               Glaciology, GEOL 4888,  Spring 2017                        Humphrey

Here are some calculations to back up some of our thoughts from the lectures.  Note question 1 takes you through the complexity of the Nye Glen flow law. This may be hard for some of you, so feel free to ask me questions. (2 points for each of the first 2 questions, none for the last)

 1. A section of glacier is being stretched, the longitudinal stress (t_xx) is 200KPa. The only stresses in the glacier are this extensional stress and the basal shear stress (t_xz) which is about 100KPa, and of course the overburden stress or pressure. The glacier is about 600m deep.

1. What is the overburden pressure? (ignore the longitudinal stress)

2. The longitudinal stress is a deviatoric stress, so what is the approximate total (non-deviatoric) stress (s_xx) near the bed?

3. Calculate the effective stress (t_effective) for use in the Nye-Glen flow law?

4. Use the effective stress from part c to calculate the shear strain rate (e_xz with a dot over it) near the bed using the full Nye-Glen flow law [ e_xz with a dot over it = A _* (t_effective)² _* t_xz ]. Assume the ice is -5C.

5. Compare the result from part d with the shear strain rate that you would calculate with the Glen flow law approximation, that doesn’t use the effective stress, but only raises the shear stress to the 3^rd power?

2. At a location in Greenland that I have worked, the mean snow temperature was -14C, and about 2 meters of snow accumulated each winter. Of that, about 30cm of the snow melted in the summer. The snow density was about 500 kg/m³. Did the snow pack ripen to about 0C by the end of the melt season? You might want to see if the cold content index “I” is greater or less than 1.

3.    Here is a puzzle for you (no points if you get the answer, no worries if you don’t).  As I mentioned in class, at the Olympics they have been known to spray antifreeze on the ski runs, when the weather gets so warm that the snow starts to melt and get slushy. If you understand the reason they do this, then you should be able to say whether it is better to use concentrated or dilute antifreeze?