Physics behind ridges and troughs

When a short or long wave trough is dug out in the jet stream it always pulls cold air from the north with it as it digs southward.
And ridging pulls air from the south norhtward. Does vorticity play a roll in this? Please explain.
 
I mean I understand rexs and omega blocks but why is warm air advection let loose in a ridging enviroment? And troughing, cold air is advected southward, and each is almost always supported by either a warm or cold front.I remind you I am still new at this, I do know alot but some basics still elude me.
 
This is a complicated subject, which isn't entirely easy to simplify (though we do in the quasigeostrophic approximation). Let's look at a few relationships...

The QG chi equation relates height changes to vorticity advection and DIFFERENTIAL thermal advection (this is, in a sense, opposite that of the QG omega equation, which relates vertical motion to thermal advection and differential vorticity advecion). Per QG, the advection of positive/cyclonic vorticity results in height falls; the advection of negative/anticyclonic vorticity results in height rises. Note that in a trough, flow is cyclonic, and flow around a ridge is anticyclonic. If a strong jet streak is rounding the base of a trough, an associated vort max (which are common with strongly-curved, 'narrow' jet streaks owing to positive contributions from shear and curvature vorticity) is likely to move with the jet streak (there are a lot of feedbacks and influences, so this is a very general case). As the vort max moves eastward, heights drop, effectively shifting the trough eastward. In addition, as the vort max moves away from a particular location, there is negative/anticyclonic vorticity advection, so heights rise. This helps a trough propagate downstream. Vort maxes are often strongly linked to jet streaks, for which there are complex interactions and processes (e.g. the inertial-convective contribution in the ageostrophic wind equation can intensify jet streaks, or even make them appear to 'backbuild', which may keep troughs from progressing too quickly).

OK, so there's the vorticity advection contribution... The QG-chi equation also relates differential thermal advection to height changes. For example, if warm-air advection is decreasing with height (which is relatively common downstream of a trough axis, where WAA is maximized in the low-levels -- 850-700mb -- and tends to become more neutral with height), heights above the level of max WAA will rise. This also holds true if cold-air advection is increasing with height. If we're looking at the 500mb level (common when looking at troughs and ridges), CAA would mean cold-air advection is increasing above 500mb. Flow aloft tends to be considerably more geostrophic, and thermal advective patterns tend to be quite a bit weaker than nearer the surface. At any rate, take, for example, a rapidly-deepening surface low in a zone of strong baroclinity (e.g. strong temperature gradient) at the inflection point of a ridge (east) and trough (west). To the east of the low, WAA decreasing with height from 850-500mb yields height rises, which would build the ridge aloft. To the weset of the low, CAA decreasing with height from 850-500mb yields heigh falls, which would act to deepen the trough aloft. Thermal wind relation tells us that where there is a strong temperature gradient in the low-level, there will be strong winds aloft. This help explain why cases of zonal, fast flow can be quite unstable, with rapid amplication of the flow not particularly uncommon.

Note that there is also a differential diabatic heating effect that can yield height falls/rises aloft. Diabatic heating decreasing with height can be viewed in a very similar like as WAA decreasing with height. So, think of a 'typical' summertime ridge, with dry grounds and sunny skies. The dry ground will act to lead to strong sensible heating (less latent heating), which may lead to rapid surface temperature rises. Meanwhile, above the boundary layer, there is no temperature rise due to insolation/sensible heating. This process yields increasing heights aloft. If you look at a mid-level heights map through a 24-hr period, you'll commonly see minor height rises during the day, and minor height falls during the night. In this manner, summertime ridges can, essentially, reinforce themselves --> warm-air aloft and subsidence in the ridge may result in clear skies and dry conditions, which then yield strong surface heating, which results in height rises aloft, reinforcing the ridge, which further discourages cloud-cover, etc.

From the QG approximation, we can include more ageostrophic response and talk about the SG (semigeostrophic) approximation. But, I think, for this purpose, QG is just fine.

EDIT: It's also important to remember that we're talking about troughs and ridges ALOFT, not at the surface! Oftentimes (particularly in the early to middle stages of a cyclone or anticyclone), the surface pattern is offset by 1/4 wavelength from the flow pattern aloft. For example, it's common for surface cyclones to be located east of a trough and west of a ridge (in the northern hemisphere), since there is large-scale vertical motion from ageostrophic curvature divergence aloft. Similarly, surface highs/ridges are common west of troughs and east of ridges, where ageostrophic curvature convergence aloft exists. If you're imagining this in your head, you should get a picture that low-level lows (hights) are 1/4 wavelength 'ahead' of upper-level troughs (ridges).
 
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