Circular travel as a definition of carving is quite a strange definition of carving imho.
Imho carving (and what you get taught while racing) means tips follows tails. Which means you are using the sidecut and camber of the ski. If you are skidding you are only using its camber and not the sidecut.
Circular travel due to skidding occurs when FS2 > FS1.
FS1 is the resultant force of the impacting snow acting on the tail end of the ski.
FS2 is the resultant force of the impacting snow acting on the leading end of the ski. When a skier skids around a turn, a reverse camber in the skies causes the skis to self-steer. Due to the curvature of the skis, the snow impacts the skis at different angles along its length. This causes the skis to self steer.
What's stated above means you simply cannot steer a ski due to rotary. Edging is always required to activate the self steering effect. Even someone who only tail kicks the ski's away with their heels or even upper body makes a turn because they push their skis on edge, even though the edge angle is extremely low.
The physics of carving is completely different to that.
This is me doing short turns on gs 35m:
This is not carving to me even though there is circular travel around the fall line due to tipping the ski on edge. This is skidding. Physics says so.
If I would activate the sidecut on that ski the turn would be much much bigger.