A viscous sea ice law as a stochastic average of plasticity

Over the last several years the applicability of viscous constitutive laws to sea ice on the geophysical scale has been questioned, because the local characteristics of sea ice deformation appear to be plastic in nature. In order to provide a more fundamental physical basis for a viscous law, this paper demonstrates that if time and/or length scales are chosen large enough, then stochastic variations in sea ice deformation rates can cause the average stress-strain rate relationship on these scales to take on viscous characteristics, even though the nonaveraged relationship is plastic in character. In particular, when a two-dimensional plastic model with an elliptical yield curve is used, the stochastically averaged stress-strain rate relationship takes the form of a viscous law with a pressure term: 〈σij〉 = 2η〈eij〉 + [(ζ - η) 〈ekk〉 - P], δtj, where angle brackets denote averages and where η and ζ are the shear and bulk viscosities, respectively. In the case of a circular yield curve, η = ζ. Examination of actual sea ice deformation time series and deformation rates simulated by red noise suggests that minimal time scales for the application of such averaging arguments can be as short as 1 day. The calculations also yield an empirical ratio between the plastic strength of the ice, P*, and the viscous parameters: η/P* ∼ ζ/P* ∼ 4.0 × 106 s. It is concluded that the viscous law, with the inclusion of a bulk viscosity and pressure term, is applicable to sea ice modeling.