In Jonathan Martin's Book "Mid-Latitude Atmospheric Dynamics" there is a chapter dedicated to anomalies of potential vorticity (PV). The scenario shown in the image below depicts a situation, where a positive PV anomaly near tropopause moves eastwards. It is argued, that there must be ascent motion downstream the anomaly and descent motion upstream:
The text is:
The structure of an upper-level, positive PV anomaly can be exploited to gain insight into the relationship between positive PV advection and cyclogenesis. Imagine a situation in which there is initially barotropic flow (i.e. there is no ∇pθ) and the isentropes are unique to individual isobars as shown in Figure 9.6(a). Now, if a positive, upper-level PV anomaly enters this domain from the west, the isentropes must deform so as to take on the characteristic structure of a positive PV anomaly. As the PV anomaly migrates eastward, adiabatic flow relative to the PV anomaly will head westward along the newly sloping isentropes. Thus, there will be upward vertical motion to the east of the anomaly and downward vertical motions to the west as shown schematically in Figure 9.6(b).
Next this picture is confirmed using the geopotential height equation:
With the definition (geostrophic) PV
this equation states simply
in Hoskins' seminal publication, this is called the "Vacuum Cleaner" effect.
My questions are:
Q1: From the first place I cannot follow, why the wind flows from East to West relative to the easterly migrating anomaly: This could only be, when the anomaly moves faster eastwards than the basic wind field (assumingly from W to E). Sounds strange...
Q2: Taking this wind direction relative to the anomaly as granted, where is there a region of positive PV advection? My blue arrow indicates this region of upward vertical motion: But since this region is completely outside the PV anomaly, there is only the undisturbed "local average" of PV - I cannot see any positive PV advection using the given wind direction: Per definition of the term "advection" we have positive advection of PV whenever
$$\vec v_g \cdot \vec \nabla PV_g < 0$$
The indicated wind directs from east to west. So to achieve positive PV advection, PV must increase in an easterly direction within the indicated area. Why should that be so?
The whole description is an absolute miracle for me...
Note: There is a link to this topic in Physics Stack Exchange. Don't know in which forum the question should be better asked and where the right experts can be found...