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The No-Slip Condition and Separation of Western Boundary Currents

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  • 1 Institut de Mécanique de Grenoble, Grenoble, France
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Abstract

The implementation of the no-slip boundary condition in numerical models of the oceans is discussed in this note. The physical issue here is to adequately represent the dynamical effect of the viscous boundary layer through the production of adverse vorticity at the coast. It is shown that the accuracy in the numerical evaluation of the boundary vorticity may influence the separation latitude of western boundary currents. Several numerical schemes for the no-slip boundary condition are investigated, including one specifically derived from simple boundary-layer theory. This simple analytical model can actually be seen as a tentative subgrid-scale parameterization of the boundary layer near the wall.

Two types of applications are presented using a quasigeostrophic model. The first one applies to an academic ocean box model forced by a sinusoidal wind. It is indeed found that the numerical scheme for the no-slip boundary condition has some influence on the western boundary current separation. The analytically derived parameterization is shown to perform at least as well as the second-order schemes. The second type of application concerns a model of the North Atlantic Ocean between 20° and 60°N. In the two North Atlantic model cases tested, the investigation reveals the no-slip boundary condition to have noticeable effects. Both lead, nonetheless, to satisfactory Gulf Strum separations.

Abstract

The implementation of the no-slip boundary condition in numerical models of the oceans is discussed in this note. The physical issue here is to adequately represent the dynamical effect of the viscous boundary layer through the production of adverse vorticity at the coast. It is shown that the accuracy in the numerical evaluation of the boundary vorticity may influence the separation latitude of western boundary currents. Several numerical schemes for the no-slip boundary condition are investigated, including one specifically derived from simple boundary-layer theory. This simple analytical model can actually be seen as a tentative subgrid-scale parameterization of the boundary layer near the wall.

Two types of applications are presented using a quasigeostrophic model. The first one applies to an academic ocean box model forced by a sinusoidal wind. It is indeed found that the numerical scheme for the no-slip boundary condition has some influence on the western boundary current separation. The analytically derived parameterization is shown to perform at least as well as the second-order schemes. The second type of application concerns a model of the North Atlantic Ocean between 20° and 60°N. In the two North Atlantic model cases tested, the investigation reveals the no-slip boundary condition to have noticeable effects. Both lead, nonetheless, to satisfactory Gulf Strum separations.

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