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

[-B' -F
Finally, we eliminate Cartesian stress components from the momentum
equations (3) and the flow rule (20-21) by substituting the equations (14-16).
At the same time, we eliminate the maximum shear stress UII using the yield
constraint (6). As a result, we obtain four equations in the four unknowns
u, v, UI, and y:
+(l+b'cos2y)--2bsin2y~+b'sin2y-+2bcos
aoI aaI 2y3
ax ax aY aY
-
-Tax - T~ (u-ug, v-vg) - mfc ( v-vg) --;;*cos 2y 32- ab sin 2y *
ax ap* a3
ab * ab a *
= -T - T (u-ug,v-v +mfc (u-u,) -- sin 2y - -cos 2y-E
ax x g aP * ax ap* aY
It is useful to rewrite the system of equations in a matrix notation by
affixing the four dependent variables into a solution vector 5:
Then in matrix form the governing equations become
where
'$2 +L?g
"X Y
+ F = Q
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