AIDJEX Bulletin #40 - Polar Science Center - University of Washington

where 1 is the two-by-two identity matrix, 0 is the two-by-two zero matrix
and
c= (41)
c=
Expansion of the determinant by cofactors leads to
det (A A_-e) = det c det C
(43)
Therefore, the roots of equation (39) may be found from
det = 0
(44)
and
det C = 0 (45)
It is interesting to note that advection has no effect on the characteristic
directions. The existence and direction of characteristic curves
depend only on properties of the yield curve and flow rule. Perhaps it is
not surprising that the water stress, Coriolis force, and other applied body
forces have no effect; but since the velocity gradient components appear in
the advection terms, it seems surprising that characteristic curves may be
found without considering this term.
The elements of the matrix arise from the stress divergence term in
the momentum balance equations. Therefore, we call the directions obtained
by satisfying equation (44) the stress characteristics. Also, we
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