[A-CG42] Science in the Arctic Region

[ACG42-P11] The question of the unbounded viscosities in the VP and EVP sea ice models

*Jinro Ukita¹, Yoshimasa Matsumura¹ (1.Atmosphere and Ocean Research Institute, The University of Tokyo)

Keywords:sea ice model, VP/EVP, rheology, viscosities

Both the bulk and shear viscosities of the viscous-plastic (VP) sea ice rheology with the elliptic yield curve are said to be unbounded as strain rates approaching to zero (Hibler, 1977, 1979). Recognizing this issue Hunke and Dukowicz (1997) subsequently developed the elastic-viscous-plastic (EVP) model. Majority of the sea ice models to date are based on either the VP or EVP rheology with the elliptic yield curve.

Noting that viscosities are not intrinsic to plastic rheology, we address the question of unbounded viscosities. Assuming only the normal flow rule and the elliptic yield curve, we can express the VP’s constitutive equation using the polar coordinate representation of the strain rate. The new expression without viscosities clearly indicates that both of the normal and maximum shear stress components are bounded above in the plastic regime. The results also reveal that the viscous regime can be added on a physical ground but not from the unboundedness of the viscosities. There also needs a reformulation of the Hibler’s original formula for the positive definite requirement of the KE equation. We will discuss mathematical details of the new expression and numerical efficiency using a simple sea ice dynamical model.