I've been researching Atmospheric Rossby waves but from the multiple sources I used they all seem to be in conflict. Some say Rossby waves are parcels of air moving from east to west due to the coriolis effect (which seems like a description for a jet stream) while others sources say it's the curving of the jet streams. I have a hard time understanding Atmospheric Rossby waves and how they affect the weather and climate.
Where to start....
If you take a look at midlatitude weather on any given day, you will find a pattern of upper tropospheric winds that look like this (source: NWS):
Notice how it looks like a wave? These are called Rossby waves. You may imagine that the jet stream is imbedded in the ups and downs of these pressure contours. If we take a look at a typical winter storm (here is a random storm from 2003):
Notice how wavy the 500 mb heights are? Don't they resemble the first figure?
Now you might say "I've seen those things and they definitely move west to east." This is true. That is because the prevailing wind is westerly (in the above examples). This can be shown in a mathematical analysis, though it should be noted that baroclinic Rossby waves (mostly in the midlatitudes) propagate slower than barotropic Rossby waves, which is what this analysis works on.
I can probably into more extensive detail about Rossby waves, but I'll just end here.