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

as well as velocity fields, we must understand also how eachoccurs. However,
the satellite images definitely show velocity, not stress, discontinuities
and so it is this field on which our primary interest is focused.
In summary, the present work is expected to provide useful information
on several questions. Our intent is to study the mathematical characteristics
of the AIDJEX model (1) to understandhow,where, andwhy discontinuities
may appear, (2) to aid in the interpretation of the numerical solutions,
(3) to learn how the material parameters affect the solutions, (4) to learn
whether or not there are response features that can be observed in the ice
cover, and (5) to determine equations along characteristic curves to allow
development of analytical solution techniques.
BACKGROUND
Our interest in the characteristic analysis was aroused by the work of
Marco and Thompson (1975, 1977), who studied the regular pattern of leads
that are sometimes observed over large portions of the Beaufort and Chukchi
Seas. Their several attempts to explain the lead patterns have led to the
conclusion that brittle material fracture is the cause. We, however, do not
share their belief that plasticity cannot describe the phenomenon. Their
analysis of mathematical characteristics associated with a plastic model
depends on a von Mises yield surface and normal flow rule that prohibits
dilatation. Theseare notproperties of the AIDJEX plastic model. It is
felt that plasticity may be able to explain the lead patterns, and the
present work does show such a possibility. However, the interpretation of
lead patterns in terms of characteristic directions by Marco and Thompson
does point toward an analysis that extends our knowledge of properties of
the AIDJEX model and, consequently, of sea ice dynamics. Therefore, we consider
their work to be of particular importance.
The method of characteristics applied to a system of first order differential
equations consists of finding the characteristic directions, or
simply the characteristics, and a differential equation for each characteristic.
When this equation is differentiated in only the characteristic
direction it is called a characteristic relation. The system of differential
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