And here is a quote from Shepherd and McLandress, 2011

In particular, the tropospheric warming that is robustly expected from climate change leads to a strengthening of the upper flanks of the subtropical jets, which causes the critical layers on the equatorward side of the jets to move upward, and with them the Rossby wave drag, allowing more Rossby wave activity to penetrate into the subtropical lower stratosphere (Figs. 4, 5). Because the subtropics represent the critical region for wave driving of the Brewer–Dobson circulation, the circulation is thereby strengthened.

So my conclusion from these two papers (there is obviously a lot more detail in the full text) is that polar vortex will weaken, subtropical jets and Brewer-Dobson circulation will strengthen, and Rossby waves will penetrate farther south. Of note, neither paper seemed (to me) to indicate that a cooler stratosphere was predicted.