Abstract
As a first step to construct the general solution of the balance and boundary conditions, two special solutions of only the balance conditions are computed.
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Notes
- 1.
See footnote 8 in Chap. 2.
- 2.
The vectors ex, ey and ez are, according to the agreement in Sect. 3.2, vectors of the one-dimensional integration cones of the integral operators \( {\partial}_x^{-1} \), \( {\partial}_y^{-1} \) and \( {\partial}_z^{-1} \). According to Sect. 3.2, these integral operators and thus all integer powers of the differential operators are defined on the ice density ρ, since this function ρ vanishes outside the finite range of glacier under consideration.
- 3.
- 4.
The designation Sb was chosen to be consistent with the designations in Sect. 8.2. This stress tensor field Sb depends on the orientation of the z-axis, but it is invariant to rotations of the coordinate system around the z-axis, because in this case the tensor components of Sbare transformed accordingly. Thus, there are actually an infinite number of stress tensor fields Sb, namely one for each orientation of the z-axis.
- 5.
The designation was Se chosen to be consistent with the designations in Sect. 8.2. The diagonal stress tensor field Se generally depends on the orientation of the coordinate system. Only in the trivial special case of horizontally homogeneous ice density and horizontal, free ice surface Se is independent of the orientation of the coordinate system and agrees with the trivial stagnant solution, where the base and integration cone vectors eishould point upwards.
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Halfar, P. (2022). Special Solutions of the Balance Conditions. In: Stresses in glaciers . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66024-9_5
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DOI: https://doi.org/10.1007/978-3-662-66024-9_5
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