What do Smoke Rings have to do with Croquet?

1061 "Windy St Lawrence" Pixels Link
There is an explanation for every line in the sky...

Smoke rings grow with time. Entropy is always increasing. But even the atmosphere has a limited vertical extent. What happens when those limits are approached? What does all of this have to do with croquet? This material has never been published. I used it operationally but that is it. There was considerable push back in the early years probably because I did not explain it well enough.

The dominant smoke ring associated with the strongest puff is what we will consider. The smoke is just there to trace the air circulation. Those movements of air occur whether or not we can see them. The deformation zone must be bowed in the direction of the strongest puff. The companion vorticity or swirl centers must straddle this strongest puff. Simple truths. 

Looking down on a quasi-horizontal
isentropic surface cross section
through a puff (large purple arrow) and
smoke ring (large companion X and N swirls)  -
 the deformation zone conceptual model
with col "C" and two outward pointing
green confluent asymptote arrows

The leading surface of the air mass being blown forward is the deformation zone veil or skin. The intersection of this deformation zone veil with the ground is the surface front. But what happens when the smoke ring expands to collide with the ground? The graphic below includes the right hand rule for each of the four legs of a more rectangular smoke ring. In previous descriptions of the smoke ring conceptual model, I had only included the companion swirls that border the puff blowing into the page at the black X. These companion vortices tend to be more meteorologically exciting but I think the top and lower branches also have a story to tell.

Looking along the puff through a vertical 
cross sectional plane perpendicular to that puff (black X in the middle) 
and smoke ring (large companion X to the left 
and N to the right) 

What happens when the smoke ring increases in size and encounters the edges of the free atmosphere. This is how that collision played out in my imagination. The primary circulation is the swirl described by the fingers of your right hand. A derivative flow indicated by the direction of the thumb results from the swirl as a form of cause and effect. 

Frictional mixing of the lowest branch of the smoke ring must occur at the earth. The primary and secondary motions of the swirl described by your right hand are reduced by friction and are certainly disrupted if not stopped all together.

Now follow the smoke ring with your right hand. Friction has eliminated the direct smoke ring flow into the rising current associated with the vorticity maximum swirl. Replacement air must be drawn inward at the base of the vorticity tube. This inward flow certainly increases the low level cyclonic vorticity in the atmospheric frame of reference.

Following the smoke ring further with your right hand, the tropopause branch of the smoke ring would be largely unaffected. The equation of continuity requires that what goes in must also go out. The swirl would produce ascending air in the relative atmosphere which enhances the contrast with the air on the other side of the deformation zone.

Making the turn downward the air following the right thumb would impact with the ground and spread out anticyclonically. The original preferred path found in the free atmosphere would be disrupted by friction and the chaos of the boundary layer that was described briefly previously. 

The branch of the smoke ring swirl has been
eliminated by friction near the earth in
the planetary boundary layer

This decay of the portion of the smoke ring encountering the friction of what meteorologists call the planetary boundary layer, turns the smoke ring into a croquet hoop. The surface front is located just beyond the hoop constructed of a cyclonic vorticity tube to the left and an anticyclonic vorticity tube to the right.

The vorticity maximum spins as a tube anchored on the surface within the dominant air mass. This vortex might actually increase aided by precipitation processes. This vortex must lie to the south of any low pressure centre analyzed on a surface map in the earth frame. Any surface front will be analyzed into the surface low and not the vorticity maximum potentially revealed by a detailed streamline analysis.

Similarly the vorticity minimum tube spins within the dominant air mass. This vorticity minimum must lie to the north of any high pressure centre analyzed on a surface map in the earth frame.

As the translation of the storm slows, the low will shift toward the atmospheric frame croquet vorticity maximum tube. Similarly any surface high will shift toward the croquet vorticity minimum tube.

The atmospheric engine enters an important stage at the smoke ring to croquet transition. The downward exhaust vortex can easily dump its flow on the earth. This flow can fan out almost without limit as the high pressure centre. The upward cyclonic portion of the atmospheric engine is very different. The cyclonic updraft is fueled by the atmospheric energy of heat and moisture released through precipitation processes. The updraft of the cyclonic swirl increases in speed requiring more replacement air to be drawn in at the ground level. Relying on physical experience and not mathematics, the inflow of air must come from larger areas near the surface. The rotation of the earth and the Coriolis force deflects these currents of air to the right. The Coriolis force increases the cyclonic rotation of the updraft vortex of the croquet hoop atmospheric engine. Wow!

Why think about these things? The conceptual models we have created are important because they reflect real life meteorology that happens every day. One can see the patterns and in an instant apply the appropriate conceptual model and understand what the atmosphere is up to. That is weather forecasting. The water vapour imagine below depicts the recent storm. Why the water vapour imagery is my favourite data source is a long story dating back to a terrific and life changing 1982 presentation by Roger Weldon. That journey will be told but not today. For now I can explain each of those lines and details but... one can simply appreciate the atmospheric processes by employing a simple conceptual model that has been developed over the years of observing the weather. The warm conveyor belt of yesterday's storm was surging through the atmospheric croquet hoop (the transparent three dimensional dark hoop) like a fire hose.

Water Vapour Easter Monday April 13th, 2020

I know some talented graphic artists and animators at COMET in Boulder Colorado who could make these concepts sing while extracting the maximum amount of science. Here is an animation of a dust devil which would be similar to what I imagine happens along the cyclonic upright of the croquet hoop.

My wife reminds me that I am retired. It is time to make coffee. Both of these statements are certainly true. But I do believe in the simple wonder of nature that surrounds us all and asking "why". I think we can find simple joy surrounded by the untold wonders of nature. Whether (weather) we fully understand these marvels does not really matter and in no way lessens our pleasure.

Warmest regards,
Phil the Forecaster

PS: Much more still to come...