More on Fronts and Frontogenesis

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More on Fronts and Frontogenesis Chapter 14 More on Fronts and Frontogenesis

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.

fvz = sx

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

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

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

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.

Frontogenesis in a deformation field y x ug = -ax v = ay Dq = 12oC

A 1000-500 mb thickness chart over Australia

The End