The Vertical Advection of Momentum in Bryan-Cox-Semtner Ocean General Circulation Models

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Abstract
This paper is concerned with the way that the Bryan-Cox-Semtner type ocean general circulation models represent the vertical advection of momentum, particularly at horizontal scales which are only slightly larger than the model grid. In practice such scales are important because limits in available computer power mean that it is often necessary to run models that only just resolve key oceanic features such as the Gulf Stream. It is shown that the approximations involved in deriving the finite-difference momentum equation lead to an error in the estimated vertical flux of momentum. It Is found that the error is largest in features that are only just resolved by the model grid and that the magnitude of the largest error increases as the grid size is reduced. As a result, in ocean models that are just eddy resolving, the error can have a significant effect on the overall balance of momentum. An improved finite-difference scheme is presented that greatly reduces the error. Abstract This paper is concerned with the way that the Bryan-Cox-Semtner type ocean general circulation models represent the vertical advection of momentum, particularly at horizontal scales which are only slightly larger than the model grid. In practice such scales are important because limits in available computer power mean that it is often necessary to run models that only just resolve key oceanic features such as the Gulf Stream. It is shown that the approximations involved in deriving the finite-difference momentum equation lead to an error in the estimated vertical flux of momentum. It Is found that the error is largest in features that are only just resolved by the model grid and that the magnitude of the largest error increases as the grid size is reduced. As a result, in ocean models that are just eddy resolving, the error can have a significant effect on the overall balance of momentum. An improved finite-difference scheme is presented that greatly reduces the error.

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