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A Nonhydrostatic Mesoscale Ocean Model. Part I: Well-Posedness and Scaling

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  • 1 Department of Geophysical Sciences, University of Chicago, Chicago, Illinois
  • | 2 Department of Computer Science, Stanford University, Stanford, California
  • | 3 Environmental Fluid Mechanics Laboratory, Stanford University, Stanford, California
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Abstract

The incompressibility and hydrostatic approximations that are traditionally used in large-scale oceanography to make the hydrodynamic equations more amenable to numerical integration result in the primitive equations. These are ill-posed in domains with open boundaries and hence not well-suited to mesoscale or regional modeling. Instead of using the hydrostatic approximation, the authors permit a greater deviation from hydrostatic balance than what exists in the ocean to obtain a system of equations that is well-posed with the specification of pointwise boundary conditions at open or solid boundaries. These equations, formulated with a free-surface boundary, model the mesoscale flow field accurately in all three-dimensions, even the vertical. It is essential to retain the vertical component of the Coriolis acceleration in the model since it is nonhydrostatic.

Abstract

The incompressibility and hydrostatic approximations that are traditionally used in large-scale oceanography to make the hydrodynamic equations more amenable to numerical integration result in the primitive equations. These are ill-posed in domains with open boundaries and hence not well-suited to mesoscale or regional modeling. Instead of using the hydrostatic approximation, the authors permit a greater deviation from hydrostatic balance than what exists in the ocean to obtain a system of equations that is well-posed with the specification of pointwise boundary conditions at open or solid boundaries. These equations, formulated with a free-surface boundary, model the mesoscale flow field accurately in all three-dimensions, even the vertical. It is essential to retain the vertical component of the Coriolis acceleration in the model since it is nonhydrostatic.

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