482 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 Reply
Gray and Killworth (1995) analyzed a simple onedimensional ice plate problem and showed that for the elliptic yield curve (Hibler 1979) the viscous–plastic sea ice rheology was linearly unstable in uniaxial divergent plastic flow. The results also demonstrated that the problem was ill posed (Strikwe...
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| Format: | Text |
| Language: | English |
| Published: |
1995
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.386.907 http://www.maths.manchester.ac.uk/~ngray/Papers/JPO_1997_27_3_reply.pdf |
| Summary: | Gray and Killworth (1995) analyzed a simple onedimensional ice plate problem and showed that for the elliptic yield curve (Hibler 1979) the viscous–plastic sea ice rheology was linearly unstable in uniaxial divergent plastic flow. The results also demonstrated that the problem was ill posed (Strikwerda 1989), as the growth rate of the instability increased with decreasing wavelength. Gray and Killworth (1995) also showed that, when the yield curve lies entirely within the third quadrant of principal stress space, these linear instabilities do not occur. They therefore suggested that the yield curve should be confined to the third quadrant to avoid illposed problems. The energy method analysis of Dukowicz (1997), and a similar two-dimensional analysis on fixed domains by Schulkes (1996), demonstrate that it is still possible to obtain properly posed problems using the elliptic yield curve when certain specific boundary conditions are applied. Strictly speaking, the results of Dukowicz only hold when the entire ice sheet is in plastic divergent or plastic convergent flow. A complete proof for a general onedimensional sea ice domain requires a treatment of the viscous transition regions between these two regimes. This is given here. Gray and Killworth (1995) showed that in one-dimension the in-plane stress N is 1 |
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