Surface ocean currents have a significant influence on the climate and their dynamics depend to a large extent on the behaviour of the vertical eddy viscosity. We present an analytic study of wind-driven surface currents for general depth-dependent vertical eddy viscosities. A novel formulation for Ekman-type flows, that relies of a transformation to polar coordinates, enables us to show that in the Northern Hemisphere the horizontal current profile decays in magnitude and turns clockwise with increasing depth, irrespective of the vertical variations in diffusivity. Using a perturbation approach, we also derive a formula for the deflection angle of the current at the surface from the wind direction and discuss its implications.

中文翻译：

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风驱动洋流的摩擦效应

表层洋流对气候有显着影响，其动力学在很大程度上取决于垂直涡粘性的行为。我们针对一般依赖于深度的垂直涡流粘度对风驱动的表面流进行了分析研究。Ekman 型流动的一种新公式依赖于极坐标的转换，使我们能够表明，在北半球，水平电流剖面在幅度上衰减并随着深度的增加顺时针旋转，而与扩散率的垂直变化无关。使用扰动方法，我们还推导出了表面电流从风向的偏转角的公式并讨论了其含义。