Mathematical Model of a Three-Dimensional Non-Isothermal Glacier

Abstract

A mathematical model is constructed for land glaciers with the thickness much less than the horizontal dimensions and radii of curvature of large bottom irregularities by means of the method of a thin boundary layer in dimensionless orthogonal coordinates. The dynamics are described by a statically determinate system of equations, so the solution for stresses is found. For the general non-isothermal case the interrelated velocity and temperature distributions are calculated by means of the iteration of solutions for velocity and for temperature. Temperature distribution is determined by a parabolic equation with a small parameter at the senior derivative. Its solution is reduced to the solution of a system of recurrent non-uniform differential equations of the first order by means of a series expansion of the small parameter. A relatively thin conducting boundary layer adjoins the upper and lower surfaces of a glacier, playing the role of a temperature damper in the ablation area. For ice divides, the statically indeterminate problem is solved, so the result for stresses depends on the temperature distribution.

A diagnostic analysis of Heinrich glacial surge events

“…Using an idea that Oerlemans [1982] had applied earlier to the much longer 100,000-year glacial cycle, MacAyeal [1993] emphasized the importance of the upward geothermal flux at the base of massive ice sheets in accounting for the necessary basal melting conditions. On the other hand, Verbitsky and Saltzman (henceforth called V-S) [1993,1994], following ideas presented earlier by Grigoryan et al [1976], suggested In the following section we present the general formula for basal temperature derived by V-S [1994] from the basic glaciological thermohydrodynamical equations. This formula is used to define two nondimensional numbers by which we can compare the magnitude of the different contributions to the basal temperature for the present and past ice sheets.…”

Mathematical Models of Ice Shelves

“…Therefore , one should distinguish various types of floating glaciers according to their dynami cs, described by different models . In this paper the symbols are mainly as in the previous paper (Grigoryan and others, 1976) so no list of symbols is provided here.…”

“…Therefore , one should distinguish various types of floating glaciers according to their dynami cs, described by different models . In this paper the symbols are mainly as in the previous paper (Grigoryan and others, 1976) so no list of symbols is provided here.• This paper was accep ted fo r the In ternat iona l Symposium on th e Th erm al R egime of Glaciers and I ce Shee ts, Burnaby, Canada, April 1975, but was not presented becau se of the absence of the a uthors . …”