I've noticed that there are saw-teeth on modern jet engines such as the GEnx and the Rolls Royce Trent 1000. What is their purpose?
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These "saw-teeth" or "chevrons" or even "acoustic liners", are there to help reduce noise generated from the operation of the engine.
As hot air from the inner core of the engine mixes with the other, cooler air, it generates noise. These "saw-teeth" are there to help smooth that mixing, thereby generating less noise which is the result of turbulence. These are seen on the Boeing 747-8 (as seen in your picture) and the Boeing 787.
The reduction of sound generated means that less noise insulation is needed for use in the fuselage of the airplane. Less insulation means less weight. Less-weight equals less fuel burn, which means that chevrons are great for passengers, and economics.
There's only one difference from your picture. As much as we would like them to blow kisses to everyone, that's not what they are there for. :)
To quote from the Wikipedia article on the subject:
In aerospace industry, chevrons are the sawtooth patterns on the trailing edges of some jet engine nozzles that are used for noise reduction. Their principle of operation is that, as hot air from the engine core mixes with cooler air blowing through the engine fan, the shaped edges serve to smooth the mixing, which reduces noise-creating turbulence. Chevrons were developed with the help of NASA. Some notable examples of such engines include GEnx and Rolls-Royce Trent 1000.