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The opening of wind-driven coastal polynyas has often been investigated using idealised flux models. Polynya flux models postulate that the boundary separating the region of thin ice adjacent to the coast within the polynya from the thicker ice piling up downstream is a mathematical shock. To conserve mass, any divergence of the ice flux across the shock translates into a change in the shock’s position or, in other words, a change in the width of the thin-ice region of the polynya. Polynya flux models are physically incomplete in that, while they conserve ice mass, they do not conserve linear momentum. In this paper, we investigate the improvements that can be achieved in the simulation of polynyas by imposing conservation of momentum as well as mass. We start by adopting a mathematically solid formulation of the ice mass and momentum balances throughout the polynya region, from the coast to the pack ice. Hydrostatic and plastic versions of the ice internal forces are used in the model. Two different approaches are then explored. We first postulate the existence of a shock at the seaward edge of the thin-ice region of the polynya and derive jump conditions for the conservation of ice mass and momentum at the shock which are consistent with the continuous model physics. Polynyas simulated by this mass- and momentum-conserving shock model always reach a steady state if the polynya forcing is uniform in space and constant in time. This is also true for all polynya flux models presented previously in the literature, but the location of the steady-state polynya edge and the time required to reach it can greatly differ between shock formulations and more simplistic flux ones. We next relax the assumption that a shock exists and let the boundary between thin ice and piling up ice emerge naturally as part of the full solution of the continuous model equations. Polynyas simulated in this way are very different from those simulated by either shock or flux models. Most notably, we find that steady-state polynya solutions are not always attainable in the continuous model. We determine under which conditions this is so and explain how such unsteady solutions come about. We also show that, in those cases when a steady-state solution exists in the continuous model, the steady-state polynya width is considerably larger than in the shock model, and the time required to attain it is accordingly longer. The occurrence of such significant differences between the polynya solutions calculated with flux and shock models, on the one hand, and with more sophisticated continuous formulations, on the other hand, suggests that the former are, at best, incomplete, and should be used with caution.
Author(s): Morales Maqueda MA, Willmott AJ, Walkington IA
Publication type: Article
Publication status: Published
Journal: Journal of Fluid Mechanics
Print publication date: 31/03/2014
ISSN (print): 0022-1120
ISSN (electronic): 1469-7645
Publisher: Cambridge University Press
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