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

MATHEMATICAL CHARACTERISTICS OF A PLASTIC MODEL
OF SEA ICE DYNAMICS
Robert S. Pritchard and R. Reimer
AIDJEX
ABSTRACT
A plastic sea ice model developed by the AIDJEX modeling group is
analyzed to determine the conditions under which real characteristic
curves exist. For this analysis, inertia and material
hardening are assumed negligible. We show that the characteristics
at each point where the material is plastic can be real and
distinct (hyperbolic equations), coincident (parabolic equations),
or imaginary (elliptic equations). There may also be elastic
regions. The characteristics enable one to see which parts of
the boundary affect which parts of the solution region, and
thereby they show where discontinuities in the solution may be
expected.
The characteristic curves do not depend on advection, air stress,
water drag, Coriolis force, sea surface tilt, or yield strength
gradients except as these terms affect the stress state. At each
point the direction taken by the characteristic curves is determined
as a function of the stress state. The curves are
symmetric about the principal stress axes, while the angle
between them depends on the position of the stress on the yield
curve. The governing set of partial differential equations are
transformed into ordinary differential equations along the characteristic
curves. These equations have been determined for an
arbitrary isotrspic yield surface and a non-normal flow rule when
advection is included.
The analytical difficulties that arise when a normal flow rule
and advection are simultaneously considered are discussed. It
has been conjectured that in many cases the large-scale lead
patterns in the ice cover are related to the characteristic
curves. Since velocity discontinuities are anticipated across
leads it is the velocity characteristics at which we look. Along
these curves there is no stretching. This physical property
neither provides a physical explanation for the correspondence
between leads and characteristics nor refutes such a possibility.
Further observations are required. The characteristic analysis
improves our understanding of the effect of yield surface and
flow rule on ice response. The characteristic equations will be
109