On the influence of frictional parameterization in wind-driven ocean circulation models

Abstract

In a series of numerical experiments the wind-driven ocean circulation is studied in an idealized, rectangular model ocean, which is forced by steady zonal winds and damped by lateral and/or bottom friction. The problem as described by the barotropic vorticity equation is characterized by a Rossby number ( R) and horizontal and/or vertical Ekman numbers ( E L, E B) only. With free-slip conditions at the boundaries steady solutions for all chosen values of R are obtained, provided the diffusivity is sufficiently large. For both the forms of frictional parameterization a northern boundary current emerges with an eastward penetration scale depending on R. The recirculation pattern in the oceanically relevant ‘intermediate’ range of R is strongly affected by the type of friction. If lateral diffusion dominates bottom friction, a strong recirculating sub-gyre emerges in the northwestern corner of the basin. Its shape resembles the vertically integrated transport fields in recent eddy resolving model (EGCM) studies. The maximum transport is increased to values several times larger than the Sverdrup transport. The increase in transport is coupled with a development of closed contours of potential vorticity, enabling a nearly free inertial flow. This behaviour provides a sharp contrast to the bottom friction case (Veronis) where inertial recirculation only takes place with values of R so large that the eastward jet reaches the eastern boundary. It is shown that the linear friction law puts a strong constraint on the flow by preventing an intense recirculation in a small part of the basin. A reduction of the diffusivity ( E L) in the lateral friction case leads to quasi-steady solutions. The interaction with eddies becomes an integral part of the time mean energetics but does not influence the recirculation character of the flow. The main conclusion of the study is that the horizontal structure of the EGCM-transport fields can be explained in terms of a steady barotropic model where lateral friction represents the dominant dissipation mechanism.