As I suspect that some people will not navigate through the Comet website, I post the following quotes and images regarding cyclogenesis from the following Comet link:
http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/navmenu.php_tab_9_page_3.1.0.htm"Six features of the large-scale tropics were identified by Gray (1968) as necessary, but not sufficient conditions for tropical cyclogenesis:
(i) sufficient ocean thermal energy [SST > 26°C to a depth of 60 m],
(ii) enhanced mid-troposphere (700 hPa) relative humidity,
(iii) conditional instability,
(iv) enhanced lower troposphere relative vorticity,
(v) weak vertical shear of the horizontal winds at the genesis site, and
(vi) displacement by at least 5° latitude away from the equator.
The first three thermodynamic parameters measure the ability to support deep convection—criteria that have been identified as seasonal indicators of genesis potential. The latter, dynamical parameters, such as vertical wind shear {see the first attached image in this post}, measure the daily likelihood of genesis. In recent years, a number of tropical cyclones have remained within 5° latitude of the equator, suggesting a need to relax this constraint. Many, but not all, of those near-equatorial systems had very small spatial scale. Locations where conditions (i) and (v) are satisfied are highlighted in {the second attached figure in the immediate prior post, ie Reply 821}.
“Necessary but not sufficient” means that all of these conditions must be present simultaneously before tropical cyclogenesis can occur, but even if all of these conditions are met, tropical cyclogenesis may not occur. Thus, the necessary, but not sufficient, criteria for tropical cyclogenesis may be summarized as the ability to support deep convection in the presence of a low-level absolute vorticity maximum. The low-level vorticity maximum reduces the local Rossby radius of deformation focusing the convective heating locally.
The ability of the initial convection to survive for many days depends on its vorticity, stability, and depth—defined by the Rossby radius of deformation, LR. The Rossby radius, LR, is the critical scale at which rotation becomes as important as buoyancy. When the disturbance size is wider than LR, it persists; systems that are smaller than LR will disperse {see the second attached image in this post}. LR is inversely proportional to latitude so it is very large in the tropics. However, the high vorticity in tropical cyclones reduces the Rossby radius and enables tropical cyclones to last for many days and even weeks.
The ability of the initial convection to survive for many days depends on its vorticity, stability, and depth—defined by the Rossby radius of deformation, LR. The Rossby radius, LR, is the critical scale at which rotation becomes as important as buoyancy. When the disturbance size is wider than LR, it persists; systems that are smaller than LR will disperse (Fig. 8.18). LR is inversely proportional to latitude so it is very large in the tropics. However, the high vorticity in tropical cyclones reduces the Rossby radius and enables tropical cyclones to last for many days and even weeks."