Abstract A 1D model, including a time variation of eddy viscosity and mixed layer depth, is applied to study Ekman spirals. It simulates a weak velocity in the atmosphere but a jet in the upper oceanic mixed layer during daytime; and a strong velocity in the atmosphere but a weak, uniform velocity in the ocean at night. The mean spirals in both atmosphere and ocean are close to the average spirals at midday and midnight, they are not flat as suggested by previous studies but consistent with the observations of Polton et al (2013) . Our results also show shorter length scale for magnitude decay than for rotation of mean velocity as observed in the ocean, which comes from the combined effects of the diurnal variation of PBL and the Coriolis force. The latter becomes more important away from the surface. In the upper oceanic mixed layer, the mean velocity mainly comes from the strong jets in the late afternoon and early evening. Near and below the depth of Ekman depth, the weak velocities change with time and cancel out each other if averaged timing is longer than the inertia period. It results in diminishing of magnitude of the mean velocity, but the amplitude of individual parcel oscillating can still be quite large near the Ekman depth. Meanwhile, the change of velocity angle from the surface is near or less than 90 degree. Hence, shorter length scale for magnitude decay than for rotation of the mean velocity is not controlled by viscosity alone. Meanwhile, the model does not need two viscosities as suggested previously. The results also show that either the diurnal variation of surface stress or eddy viscosity alone can create a diurnal oscillation of velocity in the ocean. The interactions between PBL force and the Coriolis force can create a weak instability in the atmosphere and ocean at 30° and 90°. This weak instability may explain the observed nocturnal LLJ near 30 °N on the lee of the Rocky Mountains and the intensification of mesoscale circulation simulated by Sun and Wu (1992) .

中文翻译：

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大气和海洋中埃克曼层的惯性和昼夜振荡

摘要 一个一维模型，包括涡粘性和混合层深度的时间变化，被应用于研究埃克曼螺旋。它模拟了大气中的弱速度，但在白天模拟了上层海洋混合层中的喷流；大气中的速度很强，但夜间海洋中的速度较弱，均匀。大气和海洋中的平均螺旋接近正午和午夜的平均螺旋，它们不像以前的研究表明的那样平坦，但与 Polton 等人 (2013) 的观察结果一致。我们的结果还显示，幅度衰减的长度尺度比在海洋中观察到的平均速度旋转的长度尺度更短，这是由于 PBL 的昼夜变化和科里奥利力的综合影响。远离表面，后者变得更加重要。在上大洋混合层中，平均速度主要来自下午晚些时候和傍晚的强急流。在埃克曼深度附近和以下，如果平均时间长于惯性周期，弱速度随时间变化并相互抵消。这导致平均速度的幅度减小，但在 Ekman 深度附近，单个包裹振荡的幅度仍然相当大。同时，与表面的速度角变化接近或小于90度。因此，幅度衰减比平均速度的旋转更短的长度尺度不仅仅由粘度控制。同时，该模型不需要如前所述的两个粘度。结果还表明，表面应力的昼夜变化或涡流粘度本身都可以在海洋中产生速度的昼夜振荡。PBL力和科里奥利力之间的相互作用可以在30°和90°的大气和海洋中产生微弱的不稳定性。这种微弱的不稳定性可以解释在落基山脉背风面观测到的夜间 30°N 附近的低空急流以及 Sun 和 Wu (1992) 模拟的中尺度环流的加强。