• Introduction:
  • from Chap. 14.3: convergence associated with an ageostrophic circulation intensifies a front. (divergence weakens it)
  • In Chap. 13.2, used total winds in a frontogenesis eqn.
  • In Chap. 14.4, use Q vectors to deduce ageostrophic motions. But the Q vectors are derived from geostrophic winds.

• Derivation is essentially skipped. But note the following:
  1. ageostrophic motion is parallel to contours of a variable labelled: . The direction of the motion is shown in fig. 14.8. This is defined in a vertical plane perpendicular to the front.
  2. is proportional to Q_yp (= one component of the Q vector) Hence the Q vector can deduce the ageostrophic motion.
  3. Note: In this Chapter, the Q vector is used as a scalar: that follows from choosing a natural coordinate where y' is perpendicular to a straight front. For the general case of curving fronts, and/or using a fixed coordinate frame (where y' is always directed north, say) then one needs both components of a Q vector. (Hence the name.)

• Relating Q-vectors to the frontogenesis eqn (13.2)
  • Q_yp contains both confluence (-C) and shear (-S) parts on the RHS of eqn. (13.2). But, is defined using geostrophic winds. Note that the sign is opposite between Q and C (or S).
  • Q^d_yp is just a label for the diabatic heating gradient across the front which is also in eqn. (13.2)
  • the remaining term on RHS of (13.2) is the tilting term. That term is implicit in the operator on the LHS of (14.13). To see that, look at the end of the middle row in eqn (14.7).
  • S>0 or C>0 strengthens the front, so Q_yp <0 does the same. Q_yp <0 implies that <0 as well. Recalling the patterns for figs. 14.6 and 14.7, convergence is set up at the upper right and lower left of those figs.

• Shearing effect: Cold front case (figs. 14.9 & 14.10)
  • by choice of orientation, have west winds on both sides of the front, so can neglect confluence for this discussion. hence that just leaves shearing.
  • notice tilt of isentropes (dashed lines): as x' increases, then is decreasing.
  • Since y' always points towards cold air, placing the trough at the front gives u_g <0 on the cold side and u_g >0 on the warm side.
  • hence, S>0. Similarly, Q_yp <0 so that <0. See fig. 14.10. The front is enhanced.

• Shearing effect: Warm front case (fig. 14.11)
  • by choice, confluence can be neglected again.
  • to build upon the cold front discussion, consider two different orientations of the cold air relative to the front. Specifically, how does change as one moves along the warm front but heading away from the low center:
    1. fig. 14.11a: increases, so that the low is "heading away from the coldest air"
    2. fig. 14.11b: decreases, so that the low is "heading towards the coldest air"
  • imagine a front oriented east-west. Such a front may have an easterly component of wind on the cold air side and a westerly component on the warm side.
  • in fig. 14.11a, the formulas tell us that >0 (and that S<0) so that we expect frontolysis. We can also see that by noting how the shear distorts the isentropes such that they turn to become oriented more perpendicular to the front -- weakening it.
    In vector form: u_g shear turns the vector parallel to the front.
  • in fig. 14.11b, the formulas tell us that <0 (and that S>0) so that we expect frontogenesis. We can also see that by noting how the shear distorts the isentropes such that they turn to become oriented more perpendicular to the front -- strengthening it.
    In vector form: u_g shear turns the vector perpendicular to the front.
  • with this example, we can see a powerful benefit to using the Q vector analysis. The figures 14.11a and b look rather similar but reveal opposite changes to the front.

• Pure confluence
  • confluence would be apparent from cross-isobar motion at the surface
  • at higher levels, confluence could also occur for confluent geostrophic motions, similar to what was worked out in Chap. 14.3. As we said then, the pattern is like the entrance to a jet streak.
    Recalling the jet streak, the ageostrophic circulation is a "thermally direct" pattern in the entrance region.
    We can also see a link to Chap. 12, where we repeatedly mentioned a "limiting streamline" for the warm conveyor belt ("LSW") Confluence occurs along this as well, as does a frontal zone.
  • the net result we expect is frontogenesis. The formulas for S and Q_yp confirm that intuition.
  • Here Carlson makes an important point (in italics on p. 391): the ageostrophic motions are what distort the front in a way that differs from purely geostrophic confluence. The ageostrophic circulations cause:
    1. the front to develop tilt (connecting the upper and lower regions of convergence) instead of being vertical
    2. the strongest winds ("jet" center) to migrate to the warm air side of the frontal zone.

• Some additional notes: (see Bader et al (1995) p. 143.)
  • "Where the Q-vectors have a component towards warmer air, frontogenesis [by] the geostrophic wind field is indicated"
  • "Air ascends where the Q-vectors converge"

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