In ocean models, the interaction with boundaries is often parameterized as it involves small-scale processes that are usually hard to capture in a large-scale model. However, such interactions can play important roles in the model dynamics. For example, the choice of boundary conditions (free-slip vs. no-slip) has a direct impact on the vorticity (enstrophy) budget: with no-slip boundary conditions, vorticity is injected into the system, whereas with free-slip boundary conditions, there should be no vorticity injection as long as the coastline is smooth. However, we show here that at boundary singularities (e.g., corners), vorticity is injected into the domain even for free-slip boundary conditions. In this article, we use North Brazil Current rings to better understand the dynamics of eddy-topography interaction. This complex interaction is first analyzed in terms of a point vortex interacting with a wall. Within this simplified framework, we can describe the vorticity generation mechanism as a pseudoinviscid process. To quantify this vorticity injection, we first consider the inviscid limit for which we can derive an analytical formula. This theoretical prediction is then evaluated in conventional gridded ocean models. In such models, the representation of such a “viscous” boundary interaction may be affected by the grid representation and the discretization of the advection and viscous operators.

中文翻译：

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尖锐地形特征附近的涡度动力学

在海洋模型中，与边界的相互作用通常被参数化，因为它涉及通常难以在大尺度模型中捕捉的小尺度过程。然而，这种相互作用可以在模型动力学中发挥重要作用。例如，边界条件的选择（自由滑移与无滑移）对涡度（熵）预算有直接影响：在无滑移边界条件下，涡度被注入系统，而在自由滑移边界下条件下，只要海岸线光滑，就不应该有涡流注入。然而，我们在这里展示了在边界奇点（例如，角落）处，即使对于自由滑动边界条件，涡度也被注入到域中。在本文中，我们使用北巴西洋流环来更好地了解涡旋地形相互作用的动力学。首先根据与壁相互作用的点涡流来分析这种复杂的相互作用。在这个简化的框架内，我们可以将涡度产生机制描述为一个伪无粘过程。为了量化这种涡量注入，我们首先考虑我们可以推导出解析公式的无粘性极限。然后在传统的网格海洋模型中评估该理论预测。在这样的模型中，这种“粘性”边界相互作用的表示可能会受到网格表示以及对流和粘性算子的离散化的影响。我们首先考虑可以推导出解析公式的无粘性极限。然后在传统的网格海洋模型中评估该理论预测。在这样的模型中，这种“粘性”边界相互作用的表示可能会受到网格表示以及对流和粘性算子的离散化的影响。我们首先考虑可以推导出解析公式的无粘性极限。然后在传统的网格海洋模型中评估该理论预测。在这样的模型中，这种“粘性”边界相互作用的表示可能会受到网格表示以及对流和粘性算子的离散化的影响。