1. More on Fronts and Frontogenesis
Chapter 14
More on Fronts and Frontogenesis

2. Semi-geostrophic frontogenesis
The so-called semi-geostrophic theory of frontogenesis is obtained from the unapproximated forms of the frontal equations:
in other words, we do not approximate D/Dt by Dg/Dt and therefore advection by the total wind is included.

3. fvz = sx

4. As before, cross-front thermal-wind balance  fvz = sx
Now
also

5. is the total Brunt-Väisälä frequency, rather than that based on the basic state potential temperature distribution.
To maintain thermal-wind balance ( fvz = sx )

6. This is the equation for the vertical circulation in the semi-geostrophic case.
It is elliptic provided that the so-called Ertel potential vorticity,
This condition which ensures that the flow is stable to symmetric baroclinic disturbances as discussed in a later course (Advanced Lectures on Dynamical Meteorology).
Compare with the QG-circulation equation

7. x1 x2 z z X1 X2 X x (a) (b) X = x + vg(x,z)/f
(a) The circulation in the (X, Z) plane in a region of active frontogenesis (Ql > 0). (b) The corresponding circulation in (x,z)-space. The dashed lines are lines of constant X which are close together near the surface, where there is large cyclonic vorticity.

8. Frontogenesis in a deformation fieldy x
ug = -ax v = ay
Dq = 12oC

15. A 1000-500 mb thickness chart over Australia

19. The End