Reading 4: Divergence in Natural Coordinates

A. Background

While it is easy to visualize how divergence occurs with respect to pressure patterns when there is NO Coriolis effect (air moves at right angles to pressure or height contours towards low values), how does divergence "appear" on charts on which the wind is flowing parallel (or nearly parallel) to contours.

While it is difficult to visualize this, or actually see it on charts, divergence can be conceptualized better if one transforms it into the natural coordinate system. While this is mathematically beyond the level of M200/201, we can work with the concept. (As before, divergence in natural coordinates takes the form of ∆V/∆s, and has conventional units).

B. Diffluence and Speed Divergence

The concept equation for divergence in natural coordinates is as follows:

Horizontal Divergence = Diffluence + Speed Divergence

(Note: if diffluence is negative, it is called confluence, and if speed divergence is negative it is called speed convergence). The plus sign merely means you have to consider both effects, although the algebraic sign of one or both of the terms can be negative.

Let's consider this using the 500 mb level, since that is near the Level of Non-divergence. The concept equation above should produce a value near zero, therefore, when applied to the 500 mb level.

You have enough experience with charts drawn for the middle and upper troposphere (700 mb to 200 mb) to realize that the height and wind patterns resemble sine waves, with ridges and troughs. Let's examine the trough that was associated with the storminess in Southern California on February 22, 2005.

Note that in the green shaded area the wind streamlines are generally splitting apart from trough axis to ridge axis. This is called diffluence and it is very characteristis of trough/ridge systems in the jet stream that diffluence occurs east of troughs and confluence east of ridges.

That would suggest to the eye, at least, that divergence is occuring in the green region. But this is the 500 mb level, the level at which Non-divergence should be occuring.

Note that along each streamline, however, the wind speeds are stronger near the trough axis and weaker near the ridge axis. The inset shows the streamline that stretches from A to B on the chart. You will note that speed convergence is occurring along the streamline (meaning, that the air parcels on the west side of the streamline are "catching up" to the air parcels on the east side.

Thus in the concept equation above, diffluence would have a positive sign, but there would be a negative speed divergence. At the Level of Non-Divergence, these two terms are very nearly equal in opposite, producing non-divergence.

Let's take a look at a chart in the upper troposphere.

Note first that the chart has a very similar geometry, meaning the troughs and ridges are in basically the same location as they are on the 500 mb chart, as is the jet stream (this occurs in all cases, allowing you to infer positions of jet streams and troughs and ridges in the upper troposphere simply by looking at a 500 mb chart).

Note also that diffluence is occurring in the same region as it is on the 500 mb chart. But, to some extent, so is speed convergence. At this point, we must leave the quasi-quantative discussion aside, because it turns out that in the upper troposphere the two terms generally are not that diffluence "wins" out, producing net divergence east of trough axes.

The real reasons for this will have to wait for you to have more background (e.g., M403). But, for now, this will allow us to set up some rules of thumb for divergence and convergence relative to upper waves.