This paper presents an analysis of the solutions for a steady state latent heat polynya generatedby an applied wind stress acting over a semi-enclosed channel using: (a) a dynamic–thermodynamicsea ice model, and (b) a steady state flux model. We examine what processes in the seaice model are responsible for the maintenance of the polynya and how sensitive the results areto the choice of rheological parameters. We find that when the ice is driven onshore by anapplied wind stress, a consolidated ice pack forms downwind of a zone of strong convergencein the ice velocities. The build-up of internal stresses within the consolidated ice pack becomesa crucial factor in the formation of this zone and results in a distinct polynya edge. Furthermore, within the ice pack the across-channel ice velocity varies with the across-channel distance. It isdemonstrated that provided this velocity is well represented, the steady state polynya flux modelsolutions are in close agreement with those of the sea ice model. Experiments with the sea icemodel also show that the polynya shape and area are insensitive to (a) the sea ice rheology;(b) the imposition of either free-slip or no-slip boundary conditions. These findings are usedin the development of a simplified model of the consolidated ice pack dynamics, the output ofwhich is then compared with the sea ice model results. Finally, we discuss the relevance of thisstudy for the modelling of the North Water Polynya in northern Baffin Bay.
A nonlinear, steady-state model of the North Water (NOW), the Arctic's largest polynya, is presented. The model follows in the spirit of the recently developed latent and sensible heat polynya model of Mysak and Huang, but extends it in several important ways: finite amplitude displacements of the upper-layer thickness are allowed; the channel walls diverge to the south; the sensible-heat flux from the lower layer is physically well defined in terms of a vertical entrainment velocity; and the free-drifting frazil ice to the north of the NOW ice edge is allowed to move to the right of the northerly winds. An important result found here is that with the exception of late spring, the asymptotic southern ice edge position of the NOW can be simulated in terms of a latent heat model alone. In this case, the observed equatorward curvature of the ice edge in the region adjacent to the west Greenland coast can be produced by a combination of a channel that widens in the equatorward direction, together with free-drift frazil ice motion that is to the right of the northerly winds. However, in late spring, when the heat loss to the atmosphere is reduced, the sensible heat flux plays an important role in determining the position and shape of the ice edge, particularly in the region adjacent to the west Greenland coast.
One-dimensional models for the closure of a coastal latent heat polynya due to the onshore drift of frazil ice and consolidated ice are presented in this paper. The models predict the width of a polynya during an opening and closing cycle and include the cases in which the collection thickness of consolidated new ice at the polynya edge (during opening) or at the coast (during closing) is (a) a prescribed constant or (b) parameterized in terms of the depth of frazil ice arriving at the polynya edge (during opening) or the coast (during closing) and the relative velocity of the frazil ice with respect to the “convergence boundary” (i.e., the consolidated ice during opening or the stationary coastal wall during closing). Four dimensionless parameters specify the opening and closing cycle of a polynya, and throughout most of the four-dimensional parameter space the closing timescale is shorter than the opening timescale. In this case, it is found that the heat released from the polynya to the atmosphere during opening exceeds that during closing. However, this inequality for the opening/closing heat fluxes can be reversed when the frazil ice production rate during closing exceeds that during opening. Two processes contribute to polynya closure: the onshore advection of consolidated new ice and the pileup of interior frazil ice at the coastal wall. Parameter regimes are identified where pileup of interior frazil ice at the coast plays a minor role in the closure of the polynya. The impact on the polynya closure time of rearrangement of the initial interior frazil ice distribution is also studied. It is also demonstrated that when meteorological conditions are such that the frazil ice production rate during polynya closing is negligible, the closing time is independent of the initial interior frazil ice distribution, provided that its volume per unit alongshore length is fixed and that the collection depth of consolidated new ice is constant. This invariance of the polynya closing time is found not to hold using the aforementioned parameterization for the collection depth. The model is used to simulate two opening and closing polynya events off the northern coast of Svalbard. The parameter values required for the simulations are estimated from time series of wind stress and air temperature, and the results are compared with published simulations in the refereed literature. For both events, the closing time is found to be much shorter than the opening time.
Abstract 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.
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