Hi I studied physics, including geophysical fluid dynamics, and wrote my final project on this topic. Been a while but:

Global warming on the planetary scale will mean an increase in overall temperature on earth, and a likely increase in the rate of convection of air moving from the equator to the poles.

The earth's rate of rotation won't change so the accelerating effect caused by the coriolis force will not be any different, therefore things like the jet stream will still go at the same average speed.

However, the possibly faster rate of convection from the equator to the poles will likely result in more chaotic motion in the jet stream. This is already apparent in Rossby Waves), which is basically a "concertina" effect on the jet stream caused by angular vorcity (a kind of rational momentum) being conserved as the rotational path of wind around the earth moves from a wide equatorial path to the much shorter polar path. It just all bunches in as it approaches the pole.

If convection is happening faster from the equator to the poles, there will be a more pronounced concertina effect, i.e. much larger Rossby Waves, for which the main result is Arctic air being pulled much further south than is normal. For example, large Rossby Waves are the reason for it sometimes snowing in traditionally warm countries like Greece.

So global warming could make cold weather events happen nearer to the equator, which of course will bring out all the anti-global-warming nuts who will try to use it as an excuse for denying global warming is a thing, even though the cold weather events are caused by global warming.

As for aeroplane turbulence, I think the other answer from the professional pilot said it best. The strongest air flows in the jet stream will not change their overall maximum speed because the coriolis force from earth remains the same, therefore I can't foresee much difference in turbulence, not from a change of just a few degrees C anyway. But there will be problems with having to fly through areas of hotter/colder air.