标题： 大气Ekman螺旋对于分段均匀涡旋粘度 显示英文标题

标题： The atmospheric Ekman spiral for piecewise-uniform eddy viscosity

摘要： 我们研究了具有分段均匀涡流粘度的大气Ekman流的边界值问题。 此外，我们提出了一种方法，通过将涡流粘度视为任意的阶梯函数来寻找更一般的解。 我们讨论了通过此方法获得的解的存在性和唯一性，并为涡流粘度有一个和两个“跳跃”的情况提供了详细的证明。 对于更多“跳跃”的情况，我们通过归纳法建立了结果。 此外，我们通过极化变量如涡流粘度及其变化点来研究Ekman层底部表面与地转风之间的角度。 这些计算揭示了该角度如何不同于$45^\circ$，表明$0^\circ$和$90^\circ$的极端值是可达到的，这表明偏转角的潜在范围。 显示英文摘要

摘要： We investigate the boundary-value problem of atmospheric Ekman flows with piecewise-uniform eddy viscosity. In addition we present a method for finding more general solutions by considering eddy viscosity as an arbitrary step-function. We discuss the existence and uniqueness of the solutions obtained through this method, providing detailed proofs for cases with one and two "jumps" in eddy viscosity. For scenarios with more "jumps," we establish results inductively. Furthermore, we examine the angle between the bottom surface of the Ekman layer and geostrophic winds by extremizing variables such as the eddy viscosity and its point of change. These calculations reveal how the angle can differ from $45^\circ$, demonstrating that the extreme values of $0^\circ$ and $90^\circ$ are achievable, indicating the potential range of the deflection angle.