By

Gp Capt (Dr) B Nandi

**1.** Vorticity and its relationship with divergence is best understood by Vorticity equation.one can refer any text book on Dynamic Meteorology. In cartesian coordinate (x,y,z) can be written as follows

η denotes absolute vorticity. ζ denoes relative vorticity. f is the coriolos parameter. u,v and w are the component of velocity vector **V**. ρ is density of air while ‘p’ stands for pressure o the air. First term in right hand side is **divergence** term. Second one is **tilting** term and third one is **solenoidal** term. Usually the contribution of second and last term is small and for all practical purposes can be neglected. So

The interpretation of the above equation (1) is very simple. In northern hemisphere η is positive, so following the air motion if η decreases, the over all value of right hand side becomes positive hence, the divergence term of lefthand side of the equation is positive meaning that **Divergence** is taking place. if η increases **Convergence** is taking place.

- For laminar Northerly (Nly) wind ζ=0, but following the motion coriolis parameter ‘f’ is decreasing in northern hemisphere. this means η (=0+f) is decreasing. Therefore,
**Nly wind is Diverging wind**. Wind blowing from higher latitude is diverging wind. This is called latitude effect for divergence. - By similar reasoning ,
**Sly wind is Converging wind**. Wind blowing from lower latitude is converging wind. This is latitude effect for convergence

**2.** Let us look into relative vorticity equation in natural coordinate

ζ = − ∂V/ ∂n + V/ Rs

Rs is the radius of streamline. First term is shear vorticity and second term is curvature vorticity.** Sharper** is the curvature and **stronge**r is the wind more is relative vorticity (second term).

Above is the example of cyclonic vorticity due wind shear which is decreasing in the direction of “n” coordinate. this is also called cycolnic shear

Above is the example of anticyclonic vorticity due wind shear which is increasing in the direction of “n” coordinate. this is also called anticycolnic shear

- Now we can say that when air moves from positive vorticity area to lesser positive (or negative) vorticity area it advects positive vorticity ( or can be said that air moves from high ζ to low ζ )and in that event air is Diverging. So the slogan is
**PVA (Positive Vorticity Advection) causes Divergence.** - When air moves from negative vorticity area to more negative vorticity area it advects positive vorticity ( or can be said that air moves from high ζ to low ζ )and in that event air is Diverging. So the slogan is
**PVA (Positive Vorticity Advection) causes Divergence.** - When air moves from more negative vorticity area to less negative (or positive) vorticity area it advects negative vorticity ( or can be said that air moves from low ζ to high ζ )and in that event air is Converging. So the slogan is
**NVA (Negative Vorticity Advection) causes Convergence.** - When air moves from less positive vorticity area to more positive vorticity area it advects negative vorticity ( or can be said that air moves from low ζ to high ζ )and in that event air is Converging. So the slogan is
**NVA (Negative Vorticity Advection) causes Convergence.**

**3**. Some examples are provided for weather system.

**(i)****Trough/Ridge system**

Ahead ( or right) of the trough has **Divergence** as air is moving from positive curavature vorticity area at trough to negative curvature vorticity at ridge ( case of PVA). Rear(or left) of the trough has** Convergence** air is moving from negative curavature vorticity area at ridge to positive curvature vorticity at trough ( case of NVA). Point to be noted is that in the case of North-South trough, rear of the trough has Nly wind which is diverging wind and this keeps a break on the convegence amount. Similarly, ahead of the trough has Sly wind which is converging wind and this keeps a break on the amount of divergence. Nature always follow an approach of control by providing a braking mechanism. Closeness of the curved point ie trough or ridge dominates th NVA or PVA because away the flow is more or less laminar. So caution must be exercised to evaluate the NVA or PVA, remembering the breaking mechanism of Curvature and latitude change effect. If the trough/ridge system is involved with wind shear ( like by presence of jet stream) one is required to take into consideration of shear vorticity also.

Let us look into a Longwave trough on 0000UTC,03MAY2024 at 200hPa

And let us tke a look at Water Vapour image of same time

WV image clearly show that north 30^{0}N at the rear of the trough, it is supporting distribution of moist air or in orther words intsead of subsidence there is Divergence to support vertical velocity. 45^{0}N to 30^{0}N belt at the rear of trough flow is NWly with hardly any curature voticity, thus it is a zone of divergence rather than Convergence. From 30^{0}N to 20^{0}N subsidence (yellow colour) is seen at rear of the troughline indicating aregion of Convergence in the upper troposphere. Curvature vorticity is dominant at the southern half of the longwave. Ahead of the trough cloud can be seen over Bangladesh indicating Divergence ahead of the trough.

**(ii) Wind Maxima**

Above is the example of wind Maxima. Blue region shows the maximum Isotach zone. At the rear wind is confluenting and ahead wind is difluenting. So,** RIGHT** **entrance** and **LEFT exit** zone are an area of PVA and thus of Divergence other two LEFT entrance and RIGHT exit are area of NVA and thus of Convergence. It can be noted that latittude effect gives breaking mechanism in all the four sectors. So if wind maxima is weak confluenting and difluenting effect also will be weak and thus divergence convergence will be weak.

**(iii) Elliptical circulation**

For an elliptical circulation Cyclonic curvature vorticity is maximum along the major axix. So this circulation also gets divided into four zone with SW and NE quadrants as Divergent quadrants and other two quadrants of NW and SE are quadrants of Convergence. It can be noted that Latitude effect works in unision on southern half but works as braking mechanism for norther half. One should also note that wind circulation system has depth in the atmosphere and at the same time they have slope with height. This slope gives the provision of lower level Convergent quadrant to lie beneath a divergent quadrant of upper level circulation. This combination of low level convergence and upper level divergence produces good vertical motion and weather associated with elliptical cyclonic circulation.

**(iv) Circular streamline moving EAST ward**

- This is a case of circular streamline associated with low pressure system Moving Eastward (indicated by a line arrow. The cicular ring of thick blue line indicates ring of maximum wind. As per Blaton’s equation the trajectories of the fleft half of stream line moves inward and in right half the trajectories move outward.

Right Half

Inside the ring of Maximum wind we will have NVA, as wind will be blowing from low Cyclonic shear vorticity zone to high cyclonic shear zone, thus **Convergence** will take place. Out side the ring of maximun wind on the right half, opposite will happen where wind will be blowing from high Cyclonic shear vorticity zone to low cyclonic shear zone, thus **Divergence** will take place.

Left Half

Inside the ring of Maximum wind we will have PVA, as wind will be blowing from high Cyclonic shear vorticity zone to low cyclonic shear zone, thus **Divergence** will take place. Out side the ring of maximun wind on the left half, opposite will happen where wind will be blowing from low Cyclonic shear vorticity zone to high cyclonic shear zone, thus **Convergence** will take place.

**(v) A spiral Low pressure system moving NWward**

This is a case of Low pressure of spiraling wind with one sided ring of maximun wind(Blue clour). Usually the convergence zone has the clouds (shown in green colour). No 1 denotes direct convergence zone due to spiralling in of wind No 2 denotes the cloud dueto convergence f air inside the ring of wind maxima on the right half of the low. No3 denotes convergence due to confluenting wind

Following Nwp chart shows one low pressue system

Spiralling wind system has ring of maximum wind on the right side with blue shaded wind. The cloud formed at that time is shown in the following image.

- (vi) Down stream of a low level ridge

Down stream of an ridge is a zone of NVA as minimum vorticity( negative vorticity) is at ridge. Convergence due this usually allows develpment of cumulus cloud line. Mild convergence on SWly flow has also shown such clouding. Cloud image given bellow preceeded by wind chart.

4. **Conclusion**

Understanding the relationship of Vorticity advection with divergence/convergence will go long way in understanding weather as well as predicting weather. These days good predictive charts are available as NWP product.