The basic equations - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 61

The adiabatic form of the thermodynamic equation in terms of is seen from

(2.38) and (2.26) as

D = Dt ¼ 0 ð 2 : 160 Þ

Expanding (2.160) in its Eulerian form and using the decomposition of into a

base state and a small perturbation (cf. (2.144)) we find that after multiplying the
resulting equation by g=

we get the following:

Dt þ wN 2

DB = ¼ 0 ð 2 : 161 Þ

¼ g d ð ln

frequency squared is N 2 where the Brunt-Va¨ isa¨ la¨ Þ= dz. In an adiabati-

does not vary with height, so N 2

¼ 0 and

cally stratified atmosphere

DB = Dt ¼ 0 ð 2 : 162 Þ

so that buoyancy B is conserved for air parcel motion.

2.8 SIMPLE, IDEALIZED MODELS OF DRY CONVECTION: PLUMES
AND BUBBLES

In the late 1940s and 1950s, realistic computer simulations of convective clouds
were not yet possible with the available machines. However, simple, highly
idealized models were devised, which illustrate some significant properties of
simple types of cumulus convection. Much of this work was done at Cambridge
and Imperial College in England and supported by laboratory experiments.
Prominent contributors included Richard Scorer, Bruce Morton, G. I. Taylor, J. S.
Turner, and, in the U. S., Joanne (Malkus) Simpson.
Two basic types of convection were identified: plumes and thermals. Plumes
are buoyant jets in which buoyancy is supplied steadily from a ''point'' source and
the buoyant region is continuous ( Figure 2.12a ). Examples of dry plumes include
active volcanoes, power plant/industrial smoke stacks, localized forest fires, and
heated mountain peaks during the daytime. Moist convection forced by continu-
ous mesoscale lift (e.g., along an advancing front or outflow boundary) or
pyrocumulus clouds forced over a forest fire are like plumes, though the source of
buoyancy is not exactly continuous. Thermals, on the other hand, are discrete
buoyant elements in which buoyancy is confined to the limited volume of the fluid
( Figure 2.12b ). In effect, thermals are plumes that are ''turned on'' for very short
periods of time. So, plumes result from steady heat sources, while thermals result
from heat sources turned on for very short periods of time, resulting in bursts or
''puffs'' or ''bubbles''. Thermals for moist convection are found in ''multicell'' con-
vection (to be discussed in Chapter 3). Starting plumes are plumes that are turned
on and as such are plumes with well-defined, advancing upper edges ( Figure
2.12c ). Starting plumes for moist convection may be similar to the beginning
stages of any deep convective cloud.