This article describes in basic terms the two most commonly quoted models for extratropical cyclone development (cyclogenesis).
The Norwegian Cyclone Model
Early in the 20th century, Norwegian meteorologists formulated a model for an extratropical cyclone that develops as a disturbance along the boundary (front) between the polar and mid-latitude air masses. The disturbance distorts the front into a wavelike configuration.
Wave forms on front (image source: NOAA)
As the pressure within the disturbance decreases, the disturbance assumes the appearance of a cyclone with its characteristic counter-clockwise flow. Southerly winds take warm air northward ahead of the storm and northerly winds bring cold air south behind it. Besides rotating counter-clockwise, the air also flows inward toward the center of the cyclone.
Wave intensifies (image source: NOAA)
As the cyclone intensifies, the cold air streams toward the equator faster than the warm air streams toward the pole, allowing the cold front to overtake the warm front thus forcing the warm air aloft. This produces a more complicated frontal structure called an occluded front, which separates two relatively cold air masses. The occlusion process may be followed by further storm intensification.
A mature low pressure system (image source: NOAA)
The separation of the cyclone from the warm air toward the Equator, however, eventually leads to the storm's decay and dissipation.
Dissipating stage of cyclone (image source: NOAA)
The Norwegian model still retains merit, as it is a good description for some cyclogenesis events.
A competing theory for extratropical cyclone development over the oceans, the Shapiro-Keyser model, was developed in 1990 and based on data from surface observations and aircraft to determine vertical structure of fronts in the northwest Atlantic. Its main differences with the Norwegian Cyclone Model are the fracture of the cold front, treating warm-type occlusions and warm fronts as the same, and allowing the cold front to progress through the warm sector perpendicular to the warm front. With this model, a weakness appears along the poleward portion of the cold front near the low centre (frontal fracture) and a back-bent front forms behind the low centre. The back-bent front can also be associated with the sting jet phenomenon - a short duration flow of strong winds that can reach 100 kts at surface level.
The center of the low is within a pocket of low-level warm air. This is called seclusion as the pocket of warm air has been encircled by cold air wrapping around the storm. The spiralling occluded front does not connect to the center of the low. The occlusion process is not due to the cold front catching up to the warm front; rather it is due to warm and cold air flows wrapping into the cyclone’s circulation.
These are often the rapidly developing cyclones known as “bombs”.
Keyser-Shapiro Cyclone model - Source: NOAA, 2006 (taken from wikimedia commons)
These models are only looking at low-level fronts and circulations. The jet stream and weather systems at upper-levels of the atmosphere are intimately tied in to cyclogenesis at the surface. The pressure falls at the surface are due to divergence or removal of air aloft. When this divergence aloft ceases, the surface pressures will start to rise and the cyclone will weaken and eventually dissipate.