1. Maintaining Thermal Wind Balance
isotachs
decameters
Assume that the height of the 1000 hPa surface is = 0 meters here (i.e., 500 hPa heights are equivalent to the thickness field – and thus no temperature advection). Consider the QG momentum equation (momentum advection only). At jet entrance (500 hPa) we have
winds are decreasing at 500 hPa in entrance region!
> 0 > 0
If the wind shear decreases, the temperature gradient should also decrease!

2. So… geostrophic advection pushes the jet entrance region out of thermal wind balance. NO CAN DO! The ageostrophic “RESPONSE” is EXACTLY what we need to maintain QG system. Consider QG momentum and mass conservation equations:
DIV/rising
CONV/sinking
> 0 
thus va > 0 (and max where du/dt is largest – along the jet axis)

4. Actually, two things happen in tandem here to ensure thermal wind balance:
Under the influence of the Coriolis force the southerly ageostrophic flow aloft will deflect eastward (i.e., in the direction of the zonal flow / into page) – and the northerly ageostrophic flow below will deflect westward (against the westerly flow / out of page) thereby increasing the vertical wind shear!
2. The jet entrance is marked by a thermally direct circulation (i.e., warm air rising, cold/sinking). This acts to weaken the temperature gradient.

5. AGEO-RESPONSE KEY EQNS
To diagnose the response…must look at the QGVVE and QGTE

6. Forcing vs response are generally opposite (if they weren’t – would be impossible to maintain the three bullets discussed here).
cyclonic
The forcing (geostrophic advection) aloft.
anti-cyclonic
sinking
The ageostrophic response (stretching/vertical motion)
rising

7. ENHANCEMENT/FORMATION
Geopotential heights/geostrophic streamlines/thickness (assume 1000 hPa hts are flat, i.e hPa everywhere!)
Vag<0
Vag>0 z
LEFT
300 hPa
divergence
convergence
isotachs
du/dt<0 y
JET EXIT
JET ENTRANCE x
du/dt>0
convergence
divergence
rising
sinking
RIGHT
thermally
direct
thermally
indirect
900 hPa
Vag>0
sinking
COOL SIDE OF JET
Vag<0
rising
From QG theory, if the temperature field responds (i.e., Q vector), the response has to be opposite of the geostrophic forcing as the geostrophic forcing actually knocks the QG system out of thermal wind balance (not allowed in the QG system). Hence in the confluent/deformation region of the jet entrance – we get frontogenetic forcing (increasing temperature gradient) but the vertical shear of the geostrophic wind is decreasing in time (see Dynamics II notes end of semester)! Hence – the atmosphere responds such that we get a thermally direct circulation in the jet entrance region with rising motion (cooling!) on the warm side of the jet streak and sinking motion (warming) on the cool. This response opposes the geostrophic forcing by mitigating the temperature gradient and hence keeps the flow in thermal wind balance.
Note the opposite is true in the exit region where we have diffluence and frontolysis. In this region, the Q vector forcing is the opposite – hence the vertical shear of the geostrophic wind is actually increasing in time while the temperature gradient is decreasing (again knocking the atmosphere out of thermal wind balance!). In this scenario, the response is thermally indirect with sinking motion over the warm air (hence warming) and rising motion of the cool air (thus cooling) – which enhances/restores the temperature gradient that is being destroyed by the geostrophic forcing. This response is consistent with increasing vertical shear!
WARM SIDE OF JET
LOW LEVEL JET
ENHANCEMENT/FORMATION