Before you even attempt to cartwheel in a hole you will probably need a kayak that is fairly slicey and fits you well.
The set up on the wave is crucial and is a comprimise between being drawn upstream by the towback and falling off the back of the wave. The aim is to get yourself in a static postion at the point where the bow of the boat is about to drop into the seam in the wave, (the point where the green flowing water meets the foam pile). At this point the move becomes possible.
A double pump initiates the move. Put in a strong forward stroke as you edge your kayak and try to lift your feet off the water. As the forward stroke ends and the bow leaves the water, turn the paddle movement into a reverse stroke to slice the bow down. As the bow enters the water the downstream flow will catch the bow – keep your weight forward and keep the momentum going by rotating your shoulders to face the direction you are travelling in i.e. down stream. As your body winds-up and then releases the kayak will follow planting the stern of the boat into the foam pile. As you feel the bow lifting out of the water put in a forward stroke on the up-stream side. Just before the kayak stalls and the bow comes over your head quickly twist again (to your right) to plant another reverse stroke in the water and throw the bow back down.
If your body rotation is good you can dispense with the forward strokes and depend solely on the reverse strokes. This will give the boat a 360 degree rotation on each and every paddle stroke making the cartwheel “clean”.
Keeping the boat in the wave is probably the hardest part. Correction strokes may well be needed to prevent you from being flushed off the wave or being drawn to far upstream. It is possible that over-rotation may occur as the body twist and water flow combine to push the boat vertical and into a pirouette. When the boat is sat vertical with the bow in the air it is also possible that the bow will come over your head resulting in the need for a roll.
Practice is really the key as the combination of double pump, wave size/speed and body rotation required will change from one cartwheel to the next.