### Abstract

A new model for the dynamics of sea ice is proposed. The pressure field, instead of being derived from a local rheology as in most existing models, is computed from a global optimization problem. Here the pressure is seen as emerging not from an equation of state but as a Lagrange multiplier that enforces the ice's resistance to compression while allowing divergence. The resulting variational problem is solved by minimizing the pressure globally throughout the domain, constrained by the equations of momentum and mass conservation, as well as the limits on ice concentration (which has to stay between 0 and 1). This formulation has an attractive mathematical elegance while being physically motivated. Moreover, it leads to an analytic formulation that is also easily implemented in a numerical code, which exhibits marked stability and is suited to capturing discontinuities. In order to test the theory, the equations for a one-dimensional model are cast in terms of Lagrangian mass coordinates. The solution to the minimization problem is compared to an exact analytic solution derived using jump conditions in a simple test case. Another case is examined, which is somewhat more complicated but still allows our physical intuition to verify the qualitative results of the model. Good agreement is found. A final validation is performed by a comparison with a particle-based model, which tracks individual ice floes and their inelastic interaction in a one-dimensional domain.

Original language | English (US) |
---|---|

Pages (from-to) | 543-560 |

Number of pages | 18 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 67 |

Issue number | 2 |

DOIs | |

State | Published - Dec 2006 |

### Fingerprint

### Keywords

- Ice dynamics
- Lagrangian fluid dynamics
- Rheology

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*67*(2), 543-560. https://doi.org/10.1137/040621156

**An optimization approach to modeling sea ice dynamics. Part 1 : Lagrangian framework.** / Huntley, Helga S.; Tabak, Esteban G.; Suh, Edward H.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 67, no. 2, pp. 543-560. https://doi.org/10.1137/040621156

}

TY - JOUR

T1 - An optimization approach to modeling sea ice dynamics. Part 1

T2 - Lagrangian framework

AU - Huntley, Helga S.

AU - Tabak, Esteban G.

AU - Suh, Edward H.

PY - 2006/12

Y1 - 2006/12

N2 - A new model for the dynamics of sea ice is proposed. The pressure field, instead of being derived from a local rheology as in most existing models, is computed from a global optimization problem. Here the pressure is seen as emerging not from an equation of state but as a Lagrange multiplier that enforces the ice's resistance to compression while allowing divergence. The resulting variational problem is solved by minimizing the pressure globally throughout the domain, constrained by the equations of momentum and mass conservation, as well as the limits on ice concentration (which has to stay between 0 and 1). This formulation has an attractive mathematical elegance while being physically motivated. Moreover, it leads to an analytic formulation that is also easily implemented in a numerical code, which exhibits marked stability and is suited to capturing discontinuities. In order to test the theory, the equations for a one-dimensional model are cast in terms of Lagrangian mass coordinates. The solution to the minimization problem is compared to an exact analytic solution derived using jump conditions in a simple test case. Another case is examined, which is somewhat more complicated but still allows our physical intuition to verify the qualitative results of the model. Good agreement is found. A final validation is performed by a comparison with a particle-based model, which tracks individual ice floes and their inelastic interaction in a one-dimensional domain.

AB - A new model for the dynamics of sea ice is proposed. The pressure field, instead of being derived from a local rheology as in most existing models, is computed from a global optimization problem. Here the pressure is seen as emerging not from an equation of state but as a Lagrange multiplier that enforces the ice's resistance to compression while allowing divergence. The resulting variational problem is solved by minimizing the pressure globally throughout the domain, constrained by the equations of momentum and mass conservation, as well as the limits on ice concentration (which has to stay between 0 and 1). This formulation has an attractive mathematical elegance while being physically motivated. Moreover, it leads to an analytic formulation that is also easily implemented in a numerical code, which exhibits marked stability and is suited to capturing discontinuities. In order to test the theory, the equations for a one-dimensional model are cast in terms of Lagrangian mass coordinates. The solution to the minimization problem is compared to an exact analytic solution derived using jump conditions in a simple test case. Another case is examined, which is somewhat more complicated but still allows our physical intuition to verify the qualitative results of the model. Good agreement is found. A final validation is performed by a comparison with a particle-based model, which tracks individual ice floes and their inelastic interaction in a one-dimensional domain.

KW - Ice dynamics

KW - Lagrangian fluid dynamics

KW - Rheology

UR - http://www.scopus.com/inward/record.url?scp=34247560620&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247560620&partnerID=8YFLogxK

U2 - 10.1137/040621156

DO - 10.1137/040621156

M3 - Article

VL - 67

SP - 543

EP - 560

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 2

ER -