In ancient times, pileus was the name of a brimless felt cap worn first by Greek sailors and then by Roman freed slaves. The word is now applied to the cap of a mushroom and the cloud that forms over the top of a vigorously growing cumulus cloud.
I only see the pileus a few times a year.
A pileus is a smooth cloud sometimes seen briefly over the top of a vigorously growing cumulus cloud. There were a few of them on the cumulus building around the Lake last Sunday.
A cap cloud sits over Mount Ymir
A similar looking cloud is frequently seen over the higher mountain peaks where it has the linguistically equivalent name of cap cloud. Such a cap cloud forms when a strong wind blows against the mountain and flows up and over it. Water vapour is cooled by the lifting and condenses to form the cloud. The vapour condenses on the upwind side, the resulting cloud droplets persist as the air flows across the mountain top, but then evaporate as the air flows down the lee side. As a consequence, a stationary cloud sits over the mountain top even though the wind howls though it.
The pileus forms in a similar way when the growing cumulus cloud acts as a barrier to the winds near its top. Some web sources suggest that the pileus is composed of ice crystals, however, this is rarely the case. Rather, the pileus is almost always composed of water droplets.
As moisture in the atmosphere is often in thin moist and dry layers, when the pileus forms, it too may appear laminated. The pileus is transient: the cumulus soon grows right through it and engulfs it—something a mountain cannot do to a cap cloud.
This pileus looks like an upside–down dinner plate hanging over the cumulus cloud. It has multiple layers.
Another laminated pileus hangs over cumulus growing over the mountains around the Lake.
Is this a type of lenticular cloud, a precursor to one, or the after-effect of one….or none of the above?
Margo, that is a perceptive question. Lenticular is a term long applied to lee-wave clouds: the clouds that form on the crests of the waves in the lee of mountains. They get the name in imitation of the lentil seed (as also did the lens of glasses or a camera). Generally, a minor distinction is made between the cap cloud (over a mountain) and the lee-wave clouds, the lenticulars. But, sometimes in complex terrain, as we have here, it is not possible to tell one from the other.
A pileus forms under the same conditions as do lenticular clouds, but where the barrier is a cumulus cloud rather than a mountain. Only once have I ever seen a wave cloud in the lee of a cumulus.
So, the answer to you question is that they form under the same conditions, the distinction being whether the thing deflecting the airflow is a mountain or a cumulus cloud. When you see a sky containing both wave clouds and cumulus, watch the cumulus tops for the appearance of the pileus. Note: a pileus is sometimes confused with an anvil. The distinction being that the moisture in the anvil came up through the cumulus and spread out to form a cloud layer while the moisture in the pileus was external to the cumulus.