Theory of the sea ice thickness distribution
We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution $g(h)$ due to Thorndike et al., (1975) into a Fokker-Planck like conservation law. The steady solution is $g(h) = {\cal N}(q) h^q \mathrm{e}^{-~ h/H}$, where $q$ and $H$ are e...
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ftdatacite:10.48550/arxiv.1507.05198 2023-05-15T16:39:31+02:00 Theory of the sea ice thickness distribution Toppaladoddi, Srikanth Wettlaufer, J. S. 2015 https://dx.doi.org/10.48550/arxiv.1507.05198 https://arxiv.org/abs/1507.05198 unknown arXiv https://dx.doi.org/10.1103/physrevlett.115.148501 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Atmospheric and Oceanic Physics physics.ao-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2015 ftdatacite https://doi.org/10.48550/arxiv.1507.05198 https://doi.org/10.1103/physrevlett.115.148501 2022-04-01T12:09:46Z We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution $g(h)$ due to Thorndike et al., (1975) into a Fokker-Planck like conservation law. The steady solution is $g(h) = {\cal N}(q) h^q \mathrm{e}^{-~ h/H}$, where $q$ and $H$ are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for $h \ll 1$, $g(h)$ is controlled by both thermodynamics and mechanics, whereas for $h \gg 1$ only mechanics controls $g(h)$. Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness $h$, from which we predict the observed $g(h)$. The genericity of our approach provides a framework for studying the geophysical scale structure of the ice pack using methods of broad relevance in statistical mechanics. : 3 pages, 2 figures Text ice pack Sea ice DataCite Metadata Store (German National Library of Science and Technology) |
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DataCite Metadata Store (German National Library of Science and Technology) |
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topic |
Atmospheric and Oceanic Physics physics.ao-ph FOS Physical sciences |
spellingShingle |
Atmospheric and Oceanic Physics physics.ao-ph FOS Physical sciences Toppaladoddi, Srikanth Wettlaufer, J. S. Theory of the sea ice thickness distribution |
topic_facet |
Atmospheric and Oceanic Physics physics.ao-ph FOS Physical sciences |
description |
We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution $g(h)$ due to Thorndike et al., (1975) into a Fokker-Planck like conservation law. The steady solution is $g(h) = {\cal N}(q) h^q \mathrm{e}^{-~ h/H}$, where $q$ and $H$ are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for $h \ll 1$, $g(h)$ is controlled by both thermodynamics and mechanics, whereas for $h \gg 1$ only mechanics controls $g(h)$. Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness $h$, from which we predict the observed $g(h)$. The genericity of our approach provides a framework for studying the geophysical scale structure of the ice pack using methods of broad relevance in statistical mechanics. : 3 pages, 2 figures |
format |
Text |
author |
Toppaladoddi, Srikanth Wettlaufer, J. S. |
author_facet |
Toppaladoddi, Srikanth Wettlaufer, J. S. |
author_sort |
Toppaladoddi, Srikanth |
title |
Theory of the sea ice thickness distribution |
title_short |
Theory of the sea ice thickness distribution |
title_full |
Theory of the sea ice thickness distribution |
title_fullStr |
Theory of the sea ice thickness distribution |
title_full_unstemmed |
Theory of the sea ice thickness distribution |
title_sort |
theory of the sea ice thickness distribution |
publisher |
arXiv |
publishDate |
2015 |
url |
https://dx.doi.org/10.48550/arxiv.1507.05198 https://arxiv.org/abs/1507.05198 |
genre |
ice pack Sea ice |
genre_facet |
ice pack Sea ice |
op_relation |
https://dx.doi.org/10.1103/physrevlett.115.148501 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1507.05198 https://doi.org/10.1103/physrevlett.115.148501 |
_version_ |
1766029861659344896 |