The tai chi energies are very complex and I certainly, like Donna, do not claim to know everything about them. There is a very good book by Stuart Alve Olson now out of print called The Intrinsic Energies of Tai Chi Chuan. He speaks of the many energies present in tai chi which I will list for you here. "Coiling energy" is not mentioned specifically although it certainly has it's place among many of the other energies. Here they are:
sticking, listening, interpreting, receiving, neutralizing, borrowing, issuing, enticing, raising, sinking, seizing, opening, closing, dispersing, ward-off, roll-back, press, push, pull, split, elbow-stroke, shoulder-stroke, twisting, breaking, grasping, drilling, intercepting, frozen, interrupting, inch, separating, shaky coil, playful shaky, folding up, wiping, peeling, deceptive and approaching.
As you can see, there are many and the line at which one may interpret their meaning is a bit hazy. So circular, coiling, sliding and spinning could certainly fall into many of the energies listed above. The important thing in tai chi practice is to be aware of the various energies and try to sense them as you practice form, etc. Push hands is an excellent way to learn to incorporate energies internally.