VORTICITY

by ZAMG


Development of spiral structures and the interaction of vorticity and vorticity advection

As already described in the chapter Vertical Motion - Omega Equation vorticity describes the rotation of a flow field, and is, therefore, a divergence property of the flow.

> 0 Cyclonic rotation
< 0 Anticyclonic rotation

The influence of cyclonic vorticity on an originally unformed cloud field can be shown easily:

Solid magenta lines represent a maximum of cyclonic circulation where the values are maximum in the centre and decrease to the outermost boundary. Whilst in the centre and at the boundaries no rotation acts on the cloud field, the rotation in between is such that the cloud field develops a distinct spiral structure after a period of time.

Consequently a clear interaction between the cloud-forming parameters of vorticity and vorticity advection can be observed:

If cyclonic vorticity exists within an air stream it is transported within this stream which leads to the development of a maximum of vorticity advection (PVA). Assuming sufficient humidity, cloudiness may be produced within the PVA maximum. Once this cloudiness exists the effect of rotation in the vorticity maximum leads to the formation of a spiral structure within this cloud system.

Vorticity consists of two contributing parts which allow an even deeper interpretation of typical cloud systems. These two parts can be distinguished easily if vorticiy is written in a natural coordinate system:

Therefore one part of vorticity originates from the curvature and the other one from the shear of the air flow.

Curvature vorticity

It is quite obvious that a cloud line under the influence of curvature is rotated according to the strength of curvature vorticity. There is theoretically no limit to this rotation. The typical resulting cloud features are:

Shear vorticity

A typical situation where significant shear is apparent within an air stream is a jet stream. It is obvious that a cloud line is rotated in the cyclonic part of shear but, contrary to the effect of curvature the rotation by shear is limited and cannot be large. Consequently, the typical resulting cloud features are:

Typical locations for shear and curvature vorticity

Looking at the most common streamline configuration of an upper level trough the following facts can be summarized:
There is maximaum curvature vorticity in the low centre as well as in the trough lying to the south-west. But while in the low centre curvature is the dominant feature, contributions to the vorticity in the trough area stem from both parts, curvature and shear. In the areas of the south-west stream in the leading part of the upper level trough streamlines are more rectilinear; consequently shear is the dominant feature there.

Typical cloud configurations associated with such a distribution of streamlines are:

The case study of 11 February 1997/06 UTC shows some of the features discussed.

11 February 1997/06.00 UTC - Meteosat IR image; magenta: relative vorticity 300 hPa, SatRep overlay: names of conceptual models
11 February 1997/06.00 UTC - Meteosat IR image; magenta: relative vorticity 300 hPa, blue: shear vorticity 300 hPa
In the left image relative vorticity at 300 hPa is superimposed. If compared with the image with vorticity at 500 hPa (compare Positive Vorticity Advection ) very similar results can be derived. The only difference can be detected close to the coast east of Scotland, where a vorticity maximum with a closed isoline can be identified.

The right image shows shear vorticity to total vorticity.

There are areas where both fields look very similar and which can be interpreted as situations where shear vorticity provides a large contribution. The following areas should be noted:

There are areas where the total and shear vorticity deviate from each other and which can be interpreted as situations where shear vorticity has no big influence on the total vorticity. This means that curvature vorticity must play the more important role. The following areas should be noted:

The following image has a third parameter, curvature vorticity, added.

11 February 1997/06.00 UTC - Meteosat IR image; magenta: relative vorticity 300 hPa, blue: shear vorticity 300 hPa, SatRep overlay: names of conceptual models
11 February 1997/06.00 UTC - Meteosat IR image; magenta: relative vorticity 300 hPa, brown: curvature vorticity 300 hPa, SatRep overlay: names of conceptual models
As before areas where all three parameters have a similar shape can be recognized and interpreted as areas where shear and curvature contribute equally to vorticity:

Areas where curvature vorticity deviates from shear vorticity but is very similar to the total vorticity field can be interpreted as areas where curvature is the dominant feature:

Areas where curvature vorticity deviates from the shape of shear and total vorticity can be interpreted as areas where shear plays the dominant role:

11 February 1997/06.00 UTC - Meteosat IR image; brown: curvature vorticity 300 hPa, red: positive vorticity advection (PVA) 300 hPa
11 February 1997/06.00 UTC - Meteosat IR image; blue: shear vorticity 300 hPa, red: positive vorticity advection (PVA) 300 hPa
With this deeper insight into the physical situations existing in the troposphere, even PVA maxima can be explained in terms of these situations and, hence, already provide hints to differentiate between individual conceptual models. In the demonstration case the following diagnoses can be made:
11 February 1997/12.00 UTC - Meteosat IR image
11 February 1997/18.00 UTC - Meteosat IR image
Shear vorticity at 300 hPa is also a very valuable tool to identify jet axes. Jet streams are characterized by a core of strong winds which decrease in speed to both sides leading to a cyclonic shear area on the left and an anticyclonic shear area to the right (looking in the direction of the stream). This can be described by the zeroline of shear vorticity. Another valuable tool for indicating jet axes are WV images. They show distinct elongated Black Stripes which represent sinking dry tropospheric or even stratospheric air streaming along the left or cyclonic side of the jet axis; the grey shaded bands to the right of these black strips represent the ascending warmer, more humid air on the anticyclonic side.
11 February 1997/06.00 UTC - Meteosat WV image; SatRep overlay: names of conceptual models
11 February 1997/06.00 UTC - Meteosat WV image; blue: shear vorticity 300 hPa
In the WV image of the case in question (left image), the following Black Stripes can be seen:

Consequently, the combination of both sets of information, the Black Stripes in the WV image and the zeroline of shear vorticity in the numerical model field can give more complete information about the existence of the jet streams and the location of the jet axes. Such a combination is also a tool to detect model analysis errors.

In the demonstration case (right image) the following can be observed:


INDEX OF BASICS
TEMPERATURE ADVECTION
VORTICITY ADVECTION