User:Bnland/sandbox

Exchange of Angular Momentum
Observational evidence shows that there is no significant time delay between the change of AAM and its corresponding change of LOD for periods longer than about 10 days. This implies a strong coupling between atmosphere and solid Earth due to surface friction, with a time constant of not more than about 7  days, the spindown time of the Ekman layer. This spindown time is the characteristic time for the transfer of atmospheric axial angular momentum to the Earth's surface and vice versa.

The zonal wind component on the ground which is most effective for the transfer of axial angular momentum between Earth and atmosphere is the component describing rigid rotation of the atmosphere. The zonal wind of this component has the amplitude u at the equator relative to the ground. u > 0 means superrotation; u < 0 means retrograd rotation with respect to the Earth. All other wind terms merely redistribute the AAM meridionally and become zero if averaged over the globe.

Surface friction allows the atmosphere to 'pick up' angular momentum from the Earth in the case of retrograd rotation or release it to the Earth in the case of superrotation. In the final stage, no exchange of axial angular momentum takes place. This implies that the climatic mean zonal wind component responsible for rigid rotation must be zero on the ground. Indeed, the observed meridional structure of the climatic mean zonal wind on the ground shows westerly winds (from the west) in middle and higher latitudes beyond about ± 30o latitude and easterly winds (from the east) - the trade winds - in lower latitudes. The atmosphere picks up angular momentum from the Earth at lower latitudes and transfers exactly the same amount to the Earth at higher latitudes.

Any short term fluctuation of the rigidly rotating zonal wind on the ground is therefore accompanied by a corresponding change in the length of day. If one considers the total atmosphere to rotate rigidly with velocity u (in m/s),  this value is related to the corresponding change of the length of day Δ (in msec) as

u ≃ 2.7 Δτ

The annual component of the change of the length of day of Δτ ≃ 0.34 ms corresponds then to a superrotation of u ≃ 0.9 m/s, and the semiannual component of Δτ ≃ 0.29 ms to u ≃ 0.8 m/s.