Linear well posedness of regularized equations of sea-ice dynamics
The viscous–plastic equations (VPE) of Hibler [J. Geophys. Res. 82(27), 3932–3938 (1977)] are widely adopted and used in Earth system models to represent sea-ice drift due to surface winds, ocean currents, and internal stresses. However, it has been reported by various investigators, at least in one...
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craippubl:10.1063/5.0152991 2024-02-11T10:08:31+01:00 Linear well posedness of regularized equations of sea-ice dynamics Chatta, Soufiane Khouider, Boualem Kesri, M’hamed Natural Sciences and Engineering Research Council of Canada 2023 http://dx.doi.org/10.1063/5.0152991 https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0152991/17414941/051504_1_5.0152991.pdf en eng AIP Publishing Journal of Mathematical Physics volume 64, issue 5 ISSN 0022-2488 1089-7658 Mathematical Physics Statistical and Nonlinear Physics journal-article 2023 craippubl https://doi.org/10.1063/5.0152991 2024-01-26T09:49:10Z The viscous–plastic equations (VPE) of Hibler [J. Geophys. Res. 82(27), 3932–3938 (1977)] are widely adopted and used in Earth system models to represent sea-ice drift due to surface winds, ocean currents, and internal stresses. However, it has been reported by various investigators, at least in one space dimension, that both Hibler’s original equations and their variant using a pressure replacement are ill posed in divergent flow regimes. Especially, Guba et al. [J. Phys. Oceanogr. 43(10), 2185–2199 (2013)] shows that both variants are ill-posed when the flow divergence exceeds a minimum threshold and their results seem to extend to two dimensions when a tensile cut-off is used. In particular, Hibler uses a Heaviside function cut-off for the viscosity coefficients of the VPE’s to avoid a singularity at infinity. Lemieux et al. [J. Comput. Phys. 231(17), 5926–5944 (2012)] regularized the Heaviside function by a hyperbolic tangent for numerical efficiency. Here, we show that, for periodic data, the linearized one-dimensional regularized VPE’s, in which the Heaviside function is replaced with a hyperbolic tangent, is well posed in the case of Hibler’s original equations. Moreover, we prove that the linearization procedure, for the regularized equations, is consistent, in the sense that the residual converges to zero that the perturbation of the solutions goes to zero, in suitable norms. Article in Journal/Newspaper Sea ice AIP Publishing Journal of Mathematical Physics 64 5 |
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English |
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Mathematical Physics Statistical and Nonlinear Physics |
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Mathematical Physics Statistical and Nonlinear Physics Chatta, Soufiane Khouider, Boualem Kesri, M’hamed Linear well posedness of regularized equations of sea-ice dynamics |
topic_facet |
Mathematical Physics Statistical and Nonlinear Physics |
description |
The viscous–plastic equations (VPE) of Hibler [J. Geophys. Res. 82(27), 3932–3938 (1977)] are widely adopted and used in Earth system models to represent sea-ice drift due to surface winds, ocean currents, and internal stresses. However, it has been reported by various investigators, at least in one space dimension, that both Hibler’s original equations and their variant using a pressure replacement are ill posed in divergent flow regimes. Especially, Guba et al. [J. Phys. Oceanogr. 43(10), 2185–2199 (2013)] shows that both variants are ill-posed when the flow divergence exceeds a minimum threshold and their results seem to extend to two dimensions when a tensile cut-off is used. In particular, Hibler uses a Heaviside function cut-off for the viscosity coefficients of the VPE’s to avoid a singularity at infinity. Lemieux et al. [J. Comput. Phys. 231(17), 5926–5944 (2012)] regularized the Heaviside function by a hyperbolic tangent for numerical efficiency. Here, we show that, for periodic data, the linearized one-dimensional regularized VPE’s, in which the Heaviside function is replaced with a hyperbolic tangent, is well posed in the case of Hibler’s original equations. Moreover, we prove that the linearization procedure, for the regularized equations, is consistent, in the sense that the residual converges to zero that the perturbation of the solutions goes to zero, in suitable norms. |
author2 |
Natural Sciences and Engineering Research Council of Canada |
format |
Article in Journal/Newspaper |
author |
Chatta, Soufiane Khouider, Boualem Kesri, M’hamed |
author_facet |
Chatta, Soufiane Khouider, Boualem Kesri, M’hamed |
author_sort |
Chatta, Soufiane |
title |
Linear well posedness of regularized equations of sea-ice dynamics |
title_short |
Linear well posedness of regularized equations of sea-ice dynamics |
title_full |
Linear well posedness of regularized equations of sea-ice dynamics |
title_fullStr |
Linear well posedness of regularized equations of sea-ice dynamics |
title_full_unstemmed |
Linear well posedness of regularized equations of sea-ice dynamics |
title_sort |
linear well posedness of regularized equations of sea-ice dynamics |
publisher |
AIP Publishing |
publishDate |
2023 |
url |
http://dx.doi.org/10.1063/5.0152991 https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0152991/17414941/051504_1_5.0152991.pdf |
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Sea ice |
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Sea ice |
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Journal of Mathematical Physics volume 64, issue 5 ISSN 0022-2488 1089-7658 |
op_doi |
https://doi.org/10.1063/5.0152991 |
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Journal of Mathematical Physics |
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64 |
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5 |
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1790607878942359552 |