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

which may be substituted into equation (103) to obtain
This analysis shows that at each point there are two orientations @
that satisfy equation (105) and along which there is no stretching. A comparison
of this result with equation (55) then provides the fact that$
corresponds to the directions of the velocity characteristics (K a = 3,4)
a'
and therefore that no stretching occurs along velocity characteristic curves.
The analysis, however, has not shown clearly what happens when characteristics
coincide or do not exist: 0 <
- IT/^ or 0 >
-
3~14. These special
cases are seen easily by considering the Mohr's circle for Q shown in Figure
6. (Thefollowing approach was pointed out to the authors by J. F. Nye.)
Fig. 6. Mohr's circle for stretching
tensor 0.
The construction of Mohr's circle follows standard procedures (e.g.,
Grandall and DahL, 1957). The states a and b in Figure 6 represent stretching
expressed in x,y coordinates. The points c and c' represent directions
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