The propagation of characteristics in sea-ice deformation fields

Abstract

The role of internal forces in determining the geometrical properties of local features such as leads and ridges in sea ice has been investigated. A description of the horizontal stress distribution in a granular material subject to two-dimensional deformations has been derived. The description yields expressions for the propagation of deformation characteristics in a granular deformation field with constant angle of internal friction. The characteristics are mathematical singularities interpreted as trajectories of constant state variables, e.g. ice concentration or ice thickness typified as leads, fractures, pressure and shear ridges. The derived descriptions are used to study the geometrical nature of curving and rectilinear lead patterns frequently observed in sea-ice deformation fields. An expression for the relationship between the arching (tangent angling) of characteristics and relative increase in shear (maximum shear stress) along them is derived. It is explained how the acute angle between large-scale rectilinear characteristics is related to the important mechanical property of the deformed material, the angle of internal friction. It is outlined how the derived results can be applied to study the horizontal distribution of internal forces in sea ice by using imagery data and stress measurements at one site only.