What are the key differences between warm and cold core cyclones? What is an example of each?
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Key differences are in structure, location, environments they thrive in. To compare/contrast these storms I'll use a mid-latitude cyclone for the cold core cyclone and a hurricane for the warm core cyclone.
Structure
The hurricane is nearly symmetric and devoid of fronts. The mid-latitude cyclone is asymmetric (comma shaped with a long tail) and has fronts associated with it.
Location and Movement
Hurricanes form in the tropics (but not around the Equator) and initially move from east to west with a discrete well-defined low pressure center. Hurricanes move with the wind. Mid-latitude cyclones occur in the mid-latitudes and move west to east with centers of low pressure that may dissipate and re-form further downstream. Mid-latitude storms move as temperature advection drives pressure falls ahead of the storm.
Environment
Hurricanes need warm ocean surface and weak vertical wind shear throughout the troposphere to develop. Mid-latitude storms are at home with shear and require horizontal temperature gradients to develop.
Hurricanes can transition into cold-core cyclones once they exit the tropics. It is possible, but not common, for a mid-latitude cyclone to transition into a warm-core tropical cyclone.
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$\begingroup$ Worth noting: I don't believe it's common for warm-core cyclones to transition to cold-core either. The majority of warm-core cyclones are not the big hurricanes you may first think of, which are drawn northward by the increased beta effect contribution. Additionally, while in the Atl and WPac many storms do transition, in quite a few other basins, cold-core transition is less common. And, we actually do get quite a few cold-core leftovers becoming warm-core in some basins (dtic.mil/dtic/tr/fulltext/u2/a265216.pdf suggests towards 50% in the Atlantic). $\endgroup$ Commented Feb 17, 2017 at 19:05
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$\begingroup$ @JeopardyTempest - youtube.com/… $\endgroup$– user1066Commented Nov 28, 2017 at 6:38
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$\begingroup$ @gansub: reading my comment fresh oncemore, perhaps it wasn't the clearest. Was saying that a fair percentage of (warm core) TCs do transition (mostly in WPac and Atl)... but that weaker systems are less likely to. And that in the end, the number of TCs that form from cold core becoming warm core probably isn't all that different from the number of TCs that wind up transitioning into cold core. Wasn't sure if your comment was in challenge, or just eye candy, but Sandy is certainly an interesting cold-core transition case indeed :-D $\endgroup$ Commented Dec 10, 2017 at 15:08
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1$\begingroup$ @JeopardyTempest actually it was to demonstrate the power of 3D visualization. In that video you can see some PV filaments dipping down and mixing with the PV filaments at a lower level. I do agree that weaker systems are less likely to transition. $\endgroup$– user1066Commented Dec 10, 2017 at 15:37