Mathematics of Climate Modeling pp 235-246 | Cite as

# Solvability of Ocean and Atmosphere Models

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## Abstract

The considered in the previous chapters systems of equations governing the dynamics of barotropic and two-layer baroclinic fluid belong to the class of systems which are called by the meteorologists the quasigeostrophic approximations for the description of the atmosphere dynamics. It is well known that the modern models of the general circulation of atmosphere and ocean are based on so-called primitive equations [99], which are also only some approximate form of the complete, not simplified hydrotermodynamic equation. The main simplification in them is the use instead of the total third dynamical equation (projection onto vertical axis) of its hydrostatic approximation. With the use of hydrostatic approximation for the fulfillment of the integral laws of conservation in diabatic approximation one needs to make a number of simplifications which are less essential than the hydrostatic approximation [99].

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