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

the stress characteristics, S a = 1,2. Since C is singular, equation
-a ’ -a
(106) is meaningless. However, our intuition leads us to believe that the
model should not change dramatically when a normal flow rule is introduced.
It also seems that the characteristic analysis should not become invalid.
It is felt further that the governing equations possess finite limits. Our
future efforts are aimed at determining these limits.
CONCLUSION
In the introduction to this paper five goals of this work were stated.
Although no one goal has been met entirely, there has been substantial,
progress toward all of them.
Our understanding of discontinuities has improved. We have determined
that the differential equations governing quasi-steady, rigid-plastic ice
models cannot be simply characterized because theymaybelocallyhyperbolic,
parabolic, or elliptic, depending on the state of stress (or stretching) at
each point. The ratio of shearing to dilating ocntrols the character of
the system. If shearing predominates ( ~ / < 48 < 3?r/4), the system is hyperbolic
and two distinct real characteristic directions exist, But when
dilating is predominant (either opening, 8 < ~/4, or closing, 8 > 3~/4),
the system is elliptic and no real characteristic directions exist. In the
cases of uniaxial extension (e = ~/4) and uniaxial contraction (0 = 3~/4),
the system is parabolic and one real characteristic direction occurs. The
crucial point to be made is that the plasticity model can admit discontinuous
solutions whenever real characteristic curves exist. This property is
dramatically different from other models such as viscous models which are
always elliptic during quasi-steady flow. We believe discontinuities are
necessary to allow the explanation of such diverse features as spatially
smooth velocity fields, shear ridging, and large leads formed within the
pack ice. We know of no model other than a plastic model that allows a
natural representation of all these features.
It is anticipated that interpretation of numerical solutions will be
enhanced by knowing the conditions under which discontinuities may appear.
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