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John K. Dukowicz

Abstract

Various approximations of the governing equations of compressible fluid dynamics are commonly used in both atmospheric and ocean modeling. Their main purpose is to eliminate the acoustic waves that are potentially responsible for inefficiency in the numerical solution, leaving behind gravity waves. The author carries out a detailed study of gravity wave dispersion for seven such approximations, individually and in combination, to exactly evaluate some of the often subtle errors. The atmospheric and oceanic cases are qualitatively and quantitatively different because, although they solve the same equations, their boundary conditions are entirely different and they operate in distinctly different parameter regimes. The atmospheric case is much more sensitive to approximation. The recent “unified” approximation of Arakawa and Konor is one of the most accurate. Remarkably, a simpler approximation, the combined Boussinesq–dynamically rigid approximation turns out to be exactly equivalent to the unified approximation with respect to gravity waves. The oceanic case is insensitive to the effects of any of the approximations, except for the hydrostatic approximation. The hydrostatic approximation is inaccurate at large wavenumbers in both the atmospheric and oceanic cases because it eliminates the entire buoyancy oscillation flow regime and is therefore to be restricted to low aspect ratio flows. For oceanic applications, certain approximations, such as the unified, dynamically rigid, and dynamically stiff approximations, are particularly interesting because they are accurate and approximately conserve mass, which is important for the treatment of sea level rise.

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Elizabeth C. Hunke and John K. Dukowicz

Abstract

A new discretization for the elastic–viscous–plastic (EVP) sea ice dynamics model incorporates metric terms to account for grid curvature effects in curvilinear coordinate systems. A fundamental property of the viscous–plastic ice rheology that is invariant under changes of coordinate system is utilized; namely, the work done by internal forces, to derive an energy dissipative discretization of the divergence of the stress tensor that includes metric terms. Comparisons of simulations using an older EVP numerical model with the new formulation highlight the effect of the metric terms, which can be significant when ice deformation is allowed to affect the ice strength.

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