My understanding is that it's good to look at the jet stream moving west to east. It's faster air than at the pole so keeps them containe

Sort of like how if you were on a play yard spinning wheel you'd move to the center because you'd be thrown off the closer you got the faster spinning edges.

Climate change is disrupted the jet stream in ways difficult to predict, as you point out. Were it to slow down, reverse, stop, whatever, the cold air would sink down like that from your freezer. Brrr ;)