CAPE, Shear, and the Thunderstorm

This document attempts to portray the relationship between CAPE, SHEAR and the resultant THUNDERSTORM.
 First the definitions:
 CAPE:  
The energy made available by lifting a saturated (i.e. 'cloudy') air pocket until it reaches its level of equilibrium. Assessed on a thermodynamic diagram as the area between the environment curve (Environmental Lapse Rate/ELR) & the parcel path curve.
 SHEAR: Shear in broad terms is given by the change of both wind direction and wind speed in the atmospheric environment through which the pocket (as defined above) is passing: in practical meteorology, it is often defined as the difference between the surface to 500 metre mean wind and the surface to 6 km mean wind, both expressed as vectors.
 Shear will be present in cases where the wind speed increases with height.
[ The Shear (of the horizontal wind-flow) as defined above is pertinent to the generation / enhancement of 'vertical vorticity'; It should not be confused with the shear leading to 'horizontal vorticity', which is usually measured over the lowest 3 km of the troposphere, and which plays a major part in the generation of Helicity. However, this latter quantity is also most important in studies & forecasting of severe local storms.]
 CAPE is important because it defines how vigorous the updraughts within any particular storm-complex potentially are - the stronger the updraught, then all other elements allowed for, heavy rain, large hail, squally winds etc. are on the cards. SHEAR defines what happens to the updraught as it develops, and also governs the interaction between the storm-downdraught and the storm-inflow environment.
 Because of the importance of the link between these two parameters, an attempt at unifying is contained in what is known as the BULK RICHARDSON NUMBER (BRN). This is defined as:

BRN=CAPE / (0.5 * (shear difference)^2)

(the shear difference [ or simply SHEAR ] is as defined above)
 For conceptual purposes, it is simply necessary to remember that:
 BRN is proportional to CAPE and inversely proportional to SHEAR
 For very high BRN values: the shear is too weak to stop the outflow pool of cold (downdraught) air moving quickly away from the parent updraught: new cells may form as the gravity current propagates downstream, but usually well away from the parent - and distinct from it. Also, as the updraught is quasi-zero sheared vertically, the rain shaft falls into a saturated environment (little or no evaporation possible), and there is no potential for a substantial downdraught.
 For moderate BRN values: the shear element (especially speed shear) now plays a crucial part in skewing the updraught, tilting the growing cloudy environment, allowing some or all of the precipitation shaft to fall into unsaturated air - evaporative cooling (plus precipitation drag) will generate a cold downdraught - the drier the air, the greater the potential for accelerating cold/gravity current flow. As the downdraught hits the surface, it splays out, meeting environmental inflow and generating new cells away from (but close by) the parent cell - this is the basis of the multi-cell thunderstorm.
 For low BRN values (but NOT quasi-zero numbers .. see below): Supercell storms may occur (other factors being right). The shear is now strong (and composed of both speed and significant directional components - this latter is most important), and the new/growing cell effectively forms alongside or even within the environment of the 'parent', the whole forming a steady-state system. The situation is complex though and rotation of the developing storm must be present - this is thought to be due to advection (and significant distortion / stretching) of low-level horizontal vorticity into the updraught of the storm environment, but knowledge here is still incomplete, though growing. (It is here that Helicity comes into play .... see elsewhere).
 For very low BRN values: the shear is too strong against very weak CAPE: the developing convective (cloudy) towers are ripped apart and are generally too ill-organised for persistent self-sustaining Cb development. However, note that within the environment of a tropical storm, a low BRN may be associated with organised convective 'streets'.
 The diagram below attempts to 'paint' the idea of linkage between CAPE & SHEAR; note carefully though that there are no values shown - quite deliberate as it must not be thought that there are always 'critical' values between one storm type and another: also, just because you have sufficient CAPE and SHEAR, it is also necessary to have sufficient humidity to sustain the storm through its life, and for the most severe types, an initial 'CAP' (i.e. an inhibition to surface-based convection) must be present to allow the 'loaded-gun' scenario to develop in some way (see elsewhere).
 The abbreviations have the usual meaning (re: METAR/TAF code); TN=tornadic activity possible.
(Remember, SHEAR is made up of both speed and directional components - in individual cases, each should be considered alone, as well as in concert:
The categories are not intended to have defined limits - merely illustrative of the rough combination of CAPE/SHEAR variables which give a particular type.)
Diagram CAPE vs. SHEAR