Inertia and diurnal oscillations of Ekman layers in atmosphere and ocean

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).