| Summary: | This paper develops a systematic analysis of a sea ice pack viewed as a thin layer of coherent ice floes and open water regions at the ocean surface. The pack is driven by wind stress and Coriolis force, with responsive water drag on the base of the floes. Integration of the mass and momentum balances through the layer thickness result in a two-dimensional theory for the interface between ocean and atmosphere. The theory is presented for a plane horizontal interface, but the construction is readily extended to a non-planar interface. An interacting continua framework is adopted to describe the layer mixture of ice and water, which introduces the layer thickness h and ice area fraction A as smoothly varying functions of the plane coordinate and time, on a pack length scale and weather system timescale. It is shown how an evolution equation for A which ignores ridging can lead to the area fraction exceeding unity in maintained converging flow, which is physically invalid. This is a feature and weakness of current models, and is eliminated by artificial cut-off in numerical treatments. Here we formulate a description of the ridging process which redistributes smoothly the excess horizontal ice flux into increasing thickness of a ridging zone of area fraction Ar, and a simple postulate for the vertical ridging flux yields an evolution equation for A which shows how A can approach unity asymptotically, but not exceed unity, in a maintained converging flow. This is a significant feature of the new model, and eliminates a serious physical and numerical flaw in existing models. The horizontal momentum balance involves the gradients of the extra stress integrated through the layer thickness, extra to the integrated water pressure over the depth of a local floe edge below sea level. These extra stresses are zero in diverging flow and arise as a result of interactions between floes during converging flow. It is shown precisely how a mean stress in a floe is determined by such edge tractions, and in turn provides an ...
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