The basic equations - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 69

a. The radius of the thermal increases rapidly, but then increases with time much
less rapidly.
b. The buoyancy of the thermal rapidly decreases as it rises and entrains stable
environmental air.
c. The thermal rises rapidly at first, but then slows down and eventually reverses
direction (descends) after buoyancy has decreased to zero and becomes negative.
The thermal then oscillates about a level as buoyancy becomes less negative
and then becomes positive again. Vertical velocity lags buoyancy during these
oscillations.

Experiments have been conducted by dropping discrete masses of relatively
dense fluid into a tank of less dense fluid. It was found that thermals behave like
spherical vortices, as discussed mathematically by the famous fluid dynamicist
Horace Lamb decades earlier. In a spherical vortex, donut-like flow is observed
surrounding a thermal, similar to what we see when we watch the upper edge of a
growing cumulus cloud turning inside out. A thermal may be thought of as the
leading edge of a starting plume, which looks like a buoyant mass of upward-
moving air turning inside out ( Figure 2.10 ). In a convective cloud, the act of
turning inside out is a result of baroclinically generated vorticity when positive
buoyancy in the thermal is surrounded by an environment of neutral buoyancy.
The upper edges of growing, cumuliform clouds have many small convective
dimples and a cauliflower-like appearance, which suggest small-scale turbulence.

INTRODUCTION TO RAYLEIGH-BE ´ NARD CONVECTION 2.9

In nature, buoyancy sources are frequently not localized as in plumes and
thermals, but rather are spread out over broad areas, at least in comparison with
the depth of the convecting layer. Thus, the buoyancy source is not a point, but
instead is distributed over a relatively wide area. The entire fluid therefore involves
some overturning and convection is said to have a ''global'' rather than a ''local''
character. The classic problem of determining what motions are driven in response
to the heating of an underlying surface was approached experimentally by the
French physicist Henri Be´ nard in 1900 and solved mathematically by the English
physicist and Nobel Laureate Lord Rayleigh (John William Strutt) (reported on
in 1916). (Perhaps we should refer to what has been called ''Rayleigh-Be´ nard''
convection as ''Ray-nard convection.'')
Be´ nard, using oil from a sperm whale, showed that, after a certain vertical
temperature gradient between two very closely spaced ( 1mm) parallel, horizontal
plates is exceeded, a stationary pattern of cells of rising and sinking motion (over-
turning) evolves. This pattern of cells is similar in appearance to the checkerboard
pattern of cumulus clouds often seen when the Sun heats up the ground or cold
air flows over a warm surface ( Figure 2.15 ) and is therefore worthy of considera-
tion, even though the real atmosphere does not have a solid upper boundary and
has much lower density than sperm whale oil, among other things. Lord Rayleigh