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

Although we have not studied in this work the magnitude of the discontinuities,
there is information available elsewhere on this topic.
The system of partial differential equations governing model response
has been transformed into a system of ordinary differential equations with
derivatives occurring only along characteristic curves. This analysis has
been completed for two somewhat different modifications to the rigid-plastic
AIDSEX model: (1) advection is neglected, and (2) the flow rule is modified
to be non-normal to the yield surface. We have as yet been unable to analyze
the AlDJEX model when advection is considered and a normal flow rule is
assunled.
The characteristic directions at each location depend on the stress or
stretching states. The existence and orientation of the characteristic
curves are independent of advection, air stress, water drag, Coriolis force,
sea surface tilt, and yield strength gradients, except as the terms affect
the stress state. Variations in stress along the stress characteristics,
however, is affected by these terms. Along velocity characteristic curves
there can be no stretching. Although this property does not provide a
physical explanation for a correspondence between leads and characteristics,
neither does it provide evidence that no such relationship exists. Inongoing
work we intend to study directly whether or not there is a correlation
between lead patterns and the stretching tensor. Preliminary work suggests
that during unfaxial opening, leads form orthogonally to the direction of
maximum opening. This result, however, is easily anticipated. We have not
yet found any correlation in other stretching states.
If such a correlation between lead orientations and characteristics can
be found, we intend to apply the theory to use satellite imagery to compare
with characteristic directions calculated in two-dimensional simulations of
sea ice dynamics. This will provide a simple indication of direction of
principal stress. as well as ratio of shearing to dilating 0.
Since we feel that leads would be more likely to be generated along
lines of velocity discontinuities than along stress characteristics. it is
perhaps more direct to express characteristic directions in terms of b-he
stretching tensor rather than the stress state. We have
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