The 3D Lagrangian residual velocity (LRV) is solved analytically in a narrow bay employing a vertically varying eddy viscosity coefficient. The nondimensional vertical profile of the eddy viscosity is described by a parabola that is characterized by its minimum value and the location of its symmetry axis. The results show that the LRV has similar structures as that under constant eddy viscosity coefficient when the magnitude is the same. The tidal body force that drives the residual velocity contains two terms, the advection and Stokes’ drift. The total LRV, as well as the LRV induced by each term, are very sensitive to the magnitude of the eddy viscosity coefficient, while the specific profile matters less. With a given magnitude, the specific profile of the varying eddy viscosity coefficient affects the total LRV by changing the LRV induced by the advection term. Moreover, the contribution mechanism of each component of the tidal body force to the total LRV is analyzed. The 3D LRV is mainly determined by the Stokes’ drift stress term regardless of the steepness of the across-bay topography. The depth-integrated and breadth-averaged LRV are mainly determined by the Stokes’ drift stress term with steep topography, but the Stokes’ drift contribution is no longer obvious with gentle topography.

中文翻译：

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涡流系数垂直变化的狭窄海湾中3D潮致拉格朗日剩余电流的解析解

3D拉格朗日残余速度（LRV）通过使用垂直变化的涡流粘度系数在狭窄的海湾中解析求解。涡流粘度的无量纲垂直剖面由抛物线描述，其特征在于其最小值和对称轴的位置。结果表明，当大小相同时，LRV具有与恒定涡流粘度系数下相似的结构。驱动剩余速度的潮汐力包含两个项，对流和斯托克斯漂移。总的LRV以及每个项引起的LRV对涡流粘度系数的大小非常敏感，而比轮廓的影响较小。在给定的大小下 通过改变由对流项引起的LRV，变化的涡流粘度系数的特定曲线会影响总LRV。此外，分析了潮汐力各分量对总LRV的贡献机理。3D LRV主要由Stokes漂移应力项确定，而与跨湾地形的陡度无关。深度积分和广度平均的LRV主要由陡峭地形的斯托克斯漂移应力项决定，但在平缓地形下斯托克斯的漂移贡献不再明显。