Is there a differential angular rotation on Earth?
The Earth's atmosphere rotates at more or less the same rate as the Earth as a whole. Note my use of "more or less". That does not mean exactly the same.

The air does rotate pretty much at the same rate as the Earth near the equator. These are the doldrums. Getting stuck in the doldrums was a big problem for ships in the days when ships used sails.

Moving northward or southward, the air near the surface of the Earth tends to rotate slightly less than the solid Earth's rotation rate. These are the trade winds. Sailing ships used the trade winds to go from Europe to the western hemisphere. The coriolis effect means that the trade winds stop at about 30° north and south latitude. These are the horse latitudes, another area where the atmosphere pretty much does rotates with the Earth. Sailing ships had problems here, too.

Moving even further north in the northern hemisphere / south in the southern hemisphere brings one to the region where surface winds blow predominantly from the west, so faster than the Earth's rotation rate. Sailing ships used these winds to return to Europe from the western hemisphere. Finally, even further from the equator (at roughly 60° north or south latitude), yet another transition occurs. This is the polar cell.


  So, my question is anyone aware of the differential angular rotation on Earth as a result of solid earth and fluid atmosphere interaction?


I mentioned sailing ships. People have been aware of how the winds blow locally since sailing started. People probably started sailing before they started writing. The Portuguese discovered the importance of the trade winds before Columbus sailed to the Americas.

So far I've only written about winds near the surface. The winds are different well above the surface. There are jet streams at the boundaries between where the trade winds and prevailing westerlies flow and at the boundaries of the polar cells.

The Japanese discovered these jet streams during World War II and used this to their advantage. They launched fire balloons from near Tokyo to drop a bomb on the US about three days later. Nowadays, we use the jet streams for more peaceful purposes.