The Great Gig up in the Sky, Bubble Formation - Mammatus Cloud Phenomenon

The existence of many different types of mammatus clouds, each with distinct properties and occurring in distinct environments, has given rise to multiple hypothesized formation mechanisms[citation needed], which are also relevant to other cloud forms.

One environmental trend is shared by all of the formation mechanisms hypothesized for mammatus clouds: sharp gradients in temperature, moisture and momentum (wind shear) across the anvil cloud/sub-cloud air boundary, which strongly influence interactions therein. The following are the proposed mechanisms, each described with its shortcomings:

The anvil of a cumulonimbus cloud gradually subsides as it spreads out from its source cloud. As air descends, it warms. However, the cloudy air will warm more slowly (at the moist adiabatic lapse rate) than the sub-cloud, dry air (at the dry adiabatic lapse rate). Because of the differential warming, the cloud/sub-cloud layer destabilizes and convective overturning can occur, creating a lumpy cloud-base. The problems with this theory are that there are observations of mammatus lobes that do not support the presence of strong subsidence in the lobes, and that it is difficult to separate the processes of hydrometeor fallout and cloud-base subsidence, thus rendering it unclear as to whether either process is occurring.
That said, cooling due to hydrometeor fallout is a second proposed formation mechanism. As hydrometeors fall into the dry sub-cloud air, the air containing the precipitation cools due to evaporation or sublimation. Being now cooler than the environmental air and unstable, they descend until in static equilibrium, at which point a restoring force curves the edges of the fallout back up, creating the lobed appearance. One problem with this theory is that observations show that cloud-base evaporation does not always produce mammatus. This mechanism could be responsible for the earliest stage of development, but other processes (namely process 1, above) may come into play as the lobes are formed and mature.
There may also be destabilization at cloud base due to melting. If the cloud base exists near the freezing line, then the cooling in the immediate air caused by melting can lead to convective overturning, just as in the processes above. However, this strict temperature environment is not always present.
The above processes specifically relied on the destabilization of the sub-cloud layer due to adiabatic or latent heating effects. Discounting the thermodynamical effects of hydrometeor fallout, another mechanism proposes that dynamics of the fallout alone are enough to create the lobes. Inhomogeneities in the masses of the hydrometeors along the cloud-base may cause inhomogeneous descent along the base. Frictional drag and associated eddy-like structures create the lobed appearance of the fallout. The main shortcoming of this theory is that vertical velocities in the lobes have been observed to be greater than the fall speeds of the hydrometeors within them; thus, there should be a dynamical downward forcing, as well.
Another method, that was first proposed by Kerry Emanuel, is called cloud-base detrainment instability (CDI), which acts very much like convective cloud-top entrainment. In CDI, cloudy air is mixed into the dry sub-cloud air rather than precipitating into it. The cloudy layer destabilizes due to evaporative cooling and mammatus are formed. Issues with this mechanism are that it fails to explain why mammatus are located in specific locations in the anvil rather than under the entire anvil, and it fails to explain how the mixing originates.
Clouds undergo thermal reorganization due to radiative effects as they evolve. There are a couple of ideas as to how radiation can cause mammatus to form. One is that, because clouds radiatively cool (Stefan-Boltzmann law) very efficiently at their tops, entire pockets of cool, negatively buoyant cloud can penetrate downward through the entire layer and emerge as mammatus at cloud-base. Another idea is that as the cloud-base warms due to radiative heating from land surface’s longwave emission, the base destabilizes and overturns. This method is only valid for optically thick clouds. However, the nature of anvil clouds is that they are largely made up of ice, and are therefore relatively optically thin.
Gravity waves are proposed to be the formation mechanism of linearly organized mammatus clouds. Indeed, wave patterns have been observed in the mammatus environment, but this is mostly due to gravity wave creation as a response to a convective updraft impinging upon the tropopause and spreading out in wave form over the entirety of the anvil. Therefore, this method does not explain the prevalence of mammatus clouds in one part of the anvil versus another. Furthermore, time and size scales for gravity waves and mammatus do not match up entirely. Gravity wave trains may be responsible for organizing the mammatus rather than forming them.