The Distribution of Stress, Velocity and Temperature in Glaciers
摘要
(Translated from Russian by Z. Yosida and Y. Suzuki and revised by the author) Glacier ice is, in the first approximation, an incompressible isotropic material having non-linear viscosity, and the problem of its motion may be solved on the basis of the flow theory, using relations among strain rate, stress and temperature in ice which have been established experimentally. In o:rder to determine the distribution of stress, velocity and temperature in ice of a glacier, it is necess~ry to solve the system of the following equations of the theory of continuous media: the equation of continuity, the three equations of equilibrium, the six compatibility conditions and the equation of energy. Until recently, exact apalytical solutions of the system of the above equations were known only for one and two-dimensional cases under unrealistically simplified assumptions. On the basis of new data concerning the rheological properties of ice, the existing solutions of one-dimensional problems were improved, and a solution of the problem of the distribution of stress, velocity and temperature in a non-linearly viscous ice slab was obtained for a simple laminar motion, where the dissipiation of energy and the dependency of creep rate on temperature are taken into account. For isothermal viscous ice, a solution of the two-dimensional problem w~s obtained, giving for the first time the possibility of an approximation of stress and velocity distribution in the longitudinal cross section of a glacier. I.