The basic formation mechanism involves the pushing up of air aloft as air within the cumulus cloud ascends. If the air is close to saturation, this leads to the formation of a layered cloud that resembles the cap or lenticular clouds that are generated by mountain waves as the air that flows through the ascending layer aloft follows a path similar to that generated by topography. I have tried to illustrate this below, although the perspective was such that I've probably oversimplified things.
There are some good examples in the time lapse below. The cumulus cloud can punch through the pileus layer if it has enough buoyancy.
The pileus has always been one of my favorite clouds.
Jim, always appreciate your educational moments
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