Inertial effect and its dependency on the topographic geometries in barotropic channel models under the weakly nonlinear regime

Recent studies have shown that the sensitivity of the circumpolar transport of channels to the westerlies is controlled by wind-driven gyre circulations. Although the form stress associated with the gyres has been shown to be controlled by eddies, bottom friction, and topographic width, the role of inertial effects has not been fully understood. In this study, we conduct a series of sensitivity analyses using the barotropic model with and without the advection term (hereinafter, the model without the advection term is denoted as linear model). Experiments showed that the sensitivity of the circumpolar transport decreased under the westerly winds compared to the linear model, while it increased under the easterly winds. We show that the inertial effect of western boundary currents generates anomalous anticyclonic circulations over the topography, producing the westward topographic form stress anomalies regardless of the wind directions. In addition, we discuss the sensitivity of the inertial effect mechanism to topographic height, width, and geometries. The inertial effect mechanism is robust as long as the gyre circulations dominate while its relative importance changes. We also found that the dynamics of the barotropic channel strongly depend on the geometries of geostrophic contours, f/h. Therefore, we conclude that the dynamics of barotropic channel models might be interpreted with caution to understand the dynamics of the Southern Ocean.