The Cardioid: The Basis for understanding all tornado outbreaks!

[Dave Van Grun]

This may jar a lot of people's thoughts on the matter, but I believe that a master code is associated with major tornado outbreaks and to that end I have attempted to ascertain that code. What I have discovered to my satisfaction is that the cardioid, that same underlying mathematical concept seen in the Ekman Spiral and whichj is associated with the planetary boundary layer, appears to be that relationship which both times and places tornado families within a given outbreak. To that end, I toss out this concept for anybody else to confirm this finding. Take any preferable large tornado outbreak and apply the cardioid to it to see for yourself. Now that means matching the cardioid's critical points to tornado family locations. The best example I can think of is the Browning Study of the May 26, 1963 Oklahoma outbreak. A very small outbreak but the pattern fits nearly perfectly to that of the cardioid. My findings suggest that the final storm,H-1, was 15 minutes off the perfect expectation. Please, try for yourselves to findf this application. In fact, try any outbreak. I have tried it on the Palm Sunday, April 11,1 965, Super outbreak of '74, and May 3, 1999 Oklahoma outbreak. It appears to work!

 

[Dick McGowan]

When you get this code, can you give it to me and me only? It would save me from a lot of cap busts in the future. I'll even toss you like $20 bucks if it works and an "I'm with Crazy" t-shirt too. Also, if you find it, will this code work only for outbreaks or could it find the "needle in the haystack" type of tornado days out there too? Basically I'm looking for a code that finds only tornado days or amazing structure too...thanks in advance!

 

[Darren Addy]

Dave,
Could you please expand upon or explain the exact steps involved in "trying it" to see if it works on any outbreak? I'd like to understand your methodology and what ingredients you are considering.

(Yet another posting in the inappropriate forum).

 

[Dave Van Grun]

This may jar a lot of people's thoughts on the matter, but I believe that a master code is associated with major tornado outbreaks and to that end I have attempted to ascertain that code. What I have discovered to my satisfaction is that the cardioid, that same underlying mathematical concept seen in the Ekman Spiral and whichj is associated with the planetary boundary layer, appears to be that relationship which both times and places tornado families within a given outbreak. To that end, I toss out this concept for anybody else to confirm this finding. Take any preferable large tornado outbreak and apply the cardioid to it to see for yourself. Now that means matching the cardioid's critical points to tornado family locations. The best example I can think of is the Browning Study of the May 26, 1963 Oklahoma outbreak. A very small outbreak but the pattern fits nearly perfectly to that of the cardioid. My findings suggest that the final storm,H-1, was 15 minutes off the perfect expectation. Please, try for yourselves to findf this application. In fact, try any outbreak. I have tried it on the Palm Sunday, April 11,1 965, Super outbreak of '74, and May 3, 1999 Oklahoma outbreak. It appears to work!

In continuing this post, I would recommend those interested to take a closer look at the Super outbreak event of '74, and particularly those storms associated with that squall line which produced the Morris et al tornadoes. I investigated this outbreak more closely after the Palm Sunday, April 11, 1965 to look for an undeniable aspect of series/sequencing and I believe that I have found it in these series of storms. In effect the Morris, Carlock, Lincoln, and Decatur storms appears to mathematically resemble a beginning alternating series/sequence process which most people are familiar with in the working of mechanical clocks; ESCAPEMENT. The escapement process is in effect an alternating series/sequencing process typically experienced through a ninety degree angle and that seems to be what this series appears to be: -sin,-cos,-sin,-cos, . . . In effect assessing this series process may point in showing that tornado families are indeed "placed" by the impulse which induced these, again based upon cardioid mathematics, i.e., circles to cardioid development. The Owaniko tornado therefore being the fifth storm in the sequence after Decatur is thought by this process to start the -cos sequencing aspect followed by the Charleston, Paris, and Angola events. This switches back again to a -sin series with the Continental, N. Manchester, and Swayzee storms. Interestingly, there is a statistical hoe where the fourth expected tornado should occur below the Swayzee event but which is filled by the Crawfordsville funnel cloud, a different statistic which may have thrown the whole process off balance but is more than adequate to fill the needed "tornado" location. This look at the Super outbreak concerned using the Forbes Post-Storm Survey of that event in which known members of families were eliminated from the seen so as to remove the confusion seen in the overall outbreak. By so doing, one can see the alternating nature of this outbreak of these particular storms. So take a closer look at this event as this is all in front of us and has been for over thirty-five years!

 

[Dave Van Grun]

In continuing this post, I would recommend those interested to take a closer look at the Super outbreak event of '74, and particularly those storms associated with that squall line which produced the Morris et al tornadoes. I investigated this outbreak more closely after the Palm Sunday, April 11, 1965 to look for an undeniable aspect of series/sequencing and I believe that I have found it in these series of storms. In effect the Morris, Carlock, Lincoln, and Decatur storms appears to mathematically resemble a beginning alternating series/sequence process which most people are familiar with in the working of mechanical clocks; ESCAPEMENT. The escapement process is in effect an alternating series/sequencing process typically experienced through a ninety degree angle and that seems to be what this series appears to be: -sin,-cos,-sin,-cos, . . . In effect assessing this series process may point in showing that tornado families are indeed "placed" by the impulse which induced these, again based upon cardioid mathematics, i.e., circles to cardioid development. The Owaniko tornado therefore being the fifth storm in the sequence after Decatur is thought by this process to start the -cos sequencing aspect followed by the Charleston, Paris, and Angola events. This switches back again to a -sin series with the Continental, N. Manchester, and Swayzee storms. Interestingly, there is a statistical hoe where the fourth expected tornado should occur below the Swayzee event but which is filled by the Crawfordsville funnel cloud, a different statistic which may have thrown the whole process off balance but is more than adequate to fill the needed "tornado" location. This look at the Super outbreak concerned using the Forbes Post-Storm Survey of that event in which known members of families were eliminated from the seen so as to remove the confusion seen in the overall outbreak. By so doing, one can see the alternating nature of this outbreak of these particular storms. So take a closer look at this event as this is all in front of us and has been for over thirty-five years!

Where did all ofthis come from? It came from studying an obscure tornado outbreak written up in teh magazine,WEATHERWISE, for the March 20, 1976 tornado event. Upon review of that outbreak, I noted many similarities with the J,K,L,M sequence of the Palm Sunday outbreak which I looked at afterward. IS IT POSSIBLE THAT TORNADO OUTBREAKS ARE IN MANY WAYS VERY SIMILAR TO EACH OTHER? The J,K,L,M sequence of storms is most peculiar because when you look at it and trace the results in your mind's eye, you cannot help but notice the cardioid feature in it. So, I sought an explanation for this in a meteorological sense and I may have found it in reviewing the basic equations

du/dt=-1/rhopartial pressure/partial x+fv
dv/dt=-1/rhopartial pressure/partial y-fu

which meteorologists will recognize as the Newtonian equations in balancing the pressure field and the horizontal velocity. What happens when these two are combined and then evaluated to ascertain an areal involvement? This has been applied to other weather concerns and is called a Prandtlian aspect or concern after the man who originally performed such matters. So,

d(u+v)/dt=-1/rho(partial pressure/partial x+partial pressure/partial y)-f(u-v)

solving for the term,f(u-v), subjecting this to a double integration to find the area yields the cardioid.

 

[Dave Van Grun]

Where did all ofthis come from? It came from studying an obscure tornado outbreak written up in teh magazine,WEATHERWISE, for the March 20, 1976 tornado event. Upon review of that outbreak, I noted many similarities with the J,K,L,M sequence of the Palm Sunday outbreak which I looked at afterward. IS IT POSSIBLE THAT TORNADO OUTBREAKS ARE IN MANY WAYS VERY SIMILAR TO EACH OTHER? The J,K,L,M sequence of storms is most peculiar because when you look at it and trace the results in your mind's eye, you cannot help but notice the cardioid feature in it. So, I sought an explanation for this in a meteorological sense and I may have found it in reviewing the basic equations

du/dt=-1/rhopartial pressure/partial x+fv
dv/dt=-1/rhopartial pressure/partial y-fu

which meteorologists will recognize as the Newtonian equations in balancing the pressure field and the horizontal velocity. What happens when these two are combined and then evaluated to ascertain an areal involvement? This has been applied to other weather concerns and is called a Prandtlian aspect or concern after the man who originally performed such matters. So,

d(u+v)/dt=-1/rho(partial pressure/partial x+partial pressure/partial y)-f(u-v)

solving for the term,f(u-v), subjecting this to a double integration to find the area yields the cardioid.

Upon finding this, I looked at the Palm Sunday, April 11, 1965 tornado outbreak(after Bradbury and Fujita, University of Chicago, SMRP 86) and applied the cardioid series/sequencing. Here is what I obtained


Storm Grouping x coordinate y coordinate
B,A,C -(2cosx-cos2x) (2sin x-sin2x)
D,F,E (2sin x-sin2x) -(2cosx-cos2x)
G and 2 L. Michigan spouts (2cosx-cos2x) -(2sin x-sin2x)
J,K,L,M -(2sin x-sin2x) (2cosx-cos2x)
H,I,00826,N -(2cosx-cos2x) -(2sin x-sin2x)
00626,00726,[J,K],O -(2cosx-cos2x) -(2sin x-sin2x)
L,P,Q,R -(2cosx-cos2x) -(2sin x-sin2x)

This outbreak seems therefore to be a continuous outbreak fitting the cardioid series/sequencing process. I looked for evidence of the Lake Michigan waterspouts as these should have occurred at roughly 1620 and 1640 cst over the Lake but to no avail. The difficulty rests with the WSR 57 radar's limit of about 50-55 nautical miles while the Lake is about that wide. This outbreak appears to be composed of a series process which is essentially circular with the first four sequences and finally stepped-down similar with the final three. MOST IMPORTANTLY, THIS OUTBREAK MIGHT DEMONSTRATE THE IMPORTANCE OF PRESSURE FIELD DIRECTION UPON THE AREA. The first four sequences represent a change relationship to that change in pressure field direction, south to northwest and finally north four the final three sequences. This should be deemed important to expectations for future events!

 

[Dave Van Grun]

In continuing this post, I would recommend those interested to take a closer look at the Super outbreak event of '74, and particularly those storms associated with that squall line which produced the Morris et al tornadoes. I investigated this outbreak more closely after the Palm Sunday, April 11, 1965 to look for an undeniable aspect of series/sequencing and I believe that I have found it in these series of storms. In effect the Morris, Carlock, Lincoln, and Decatur storms appears to mathematically resemble a beginning alternating series/sequence process which most people are familiar with in the working of mechanical clocks; ESCAPEMENT. The escapement process is in effect an alternating series/sequencing process typically experienced through a ninety degree angle and that seems to be what this series appears to be: -sin,-cos,-sin,-cos, . . . In effect assessing this series process may point in showing that tornado families are indeed "placed" by the impulse which induced these, again based upon cardioid mathematics, i.e., circles to cardioid development. The Owaniko tornado therefore being the fifth storm in the sequence after Decatur is thought by this process to start the -cos sequencing aspect followed by the Charleston, Paris, and Angola events. This switches back again to a -sin series with the Continental, N. Manchester, and Swayzee storms. Interestingly, there is a statistical hoe where the fourth expected tornado should occur below the Swayzee event but which is filled by the Crawfordsville funnel cloud, a different statistic which may have thrown the whole process off balance but is more than adequate to fill the needed "tornado" location. This look at the Super outbreak concerned using the Forbes Post-Storm Survey of that event in which known members of families were eliminated from the seen so as to remove the confusion seen in the overall outbreak. By so doing, one can see the alternating nature of this outbreak of these particular storms. So take a closer look at this event as this is all in front of us and has been for over thirty-five years!

For another example, take a look at the Oklahoma outbreak May 3, 1999. it is on the web and is noted as Storms A,B,C,D,E,G,H, and I. From a series/sequence posture it would look like a -sin,sin,sin , . . sequence with A,B,C,D; E,G,H; and I conforming to this process. In many ways these Storms A through D look like those storms associated with the Super outbreak known as the Depauw, Orleans, Fountaintown ,and Xenia events, a similar -sin sequence, The series E,G,H; and I both are of the sin sequence and seen earlier in the D,F,E seuqnce of Palm Sunday, April 11, 1965 , supporting the change in pressure field direction with tornado area involvement. Could it all be that simple?

 

[David Wolfson]

Without going back to your sources to decipher the sequences you refer to, or seeing any diagrams it sounds like you're describing projections of tornado path sequences produced by cyclic supercells. I think you're probably referring geometrically more to cycloids rather than cardioids.

If so then it makes sense that a cyclic supercell would kinda-sorta project its tornados in a cycloid pattern as its updraft rotation follows a linear path. I'm dubious that there's much predictive value in the observation except at very small time and spatial scales where you might be able to estimate successive tornado paths. You'd have to, I think, have near real-time fine-grained info, i.e. from a DOW, to do some good. IMO, FWIW.

 

[scott r currens]

Maybe we should run a few chase cases and see how well you do with the method of prediction.

 

[Bob Hartig]

Dave, you're going to get shredded on this forum the way you're going. I think you've gotten a couple valuable pointers in the responses, though, if you really want to make a case for yourself:
1) Put your ideas all down in a single paper, and break it down into meaningful language. Not everyone here is a mathematician.
2) Show the proof of it in some test cases. The burden of proof lies with you, not others to "try it and see." Try what? Without intending any insult, I truly don't have a clue what you're talking about.

 

[Ryan Wichman]

So does this sin, -sin only happen in "super outbreaks"?
What about long lived supercells? ie...the six state supercell a few years ago that went from OK to MI? Or as another famous example...Greensburg Supercell which had multiple tornadoes on the ground at one time. Does this theory satisfy those cases?

 

[Skip Talbot]

<Random math jargon> + <Random tornado events> = all tornadoes in an outbreak fall on a simple curve

I suspect this is a joke, but it is interesting to note that tornadoes and their parent supercells and weather systems have various fractal structures within them. The cardioid shape mentioned by Professor Crackpot here is a common shape found in the Mandelbrot fractal. If you could take an infinitely high resolution radar scan of a hook echo you'd probably see similar patterns in the scan's vorticies as you would see spirals on an arm of the Mandelbrot. Zooming in to look at the subvortices within vorticies you'd see self similarity and repeating spiral patterns at different levels, which is exactly what a fractal is. There is plenty of turbulence and outside influence in a hook though, so the pattern wouldn't be perfect and probably breaks down quickly instead of going infinitely deep like the Mandelbrot set does. This is also why its easy to see that our professor's theory is probably a little cracked. There is too much chaos in the system to pin tornadoes to a simple parametric curve. Despite the resemblance of some known curves and fractals, I doubt there is any real potential for prediction here. It is, however, another way to admire the awesome beauty of these phenomna.

 

[Joshua Nall]

For another example, take a look at the Oklahoma outbreak May 3, 1999. it is on the web and is noted as Storms A,B,C,D,E,G,H, and I. From a series/sequence posture it would look like a -sin,sin,sin , . . sequence with A,B,C,D; E,G,H; and I conforming to this process. In many ways these Storms A through D look like those storms associated with the Super outbreak known as the Depauw, Orleans, Fountaintown ,and Xenia events, a similar -sin sequence, The series E,G,H; and I both are of the sin sequence and seen earlier in the D,F,E seuqnce of Palm Sunday, April 11, 1965 , supporting the change in pressure field direction with tornado area involvement. Could it all be that simple?

What kinda sin are you talking about? I go to church and I know all sin is bad, so sin in sequence would be very bad. Does the -sin take away the original sin? Never knew storms could sin too.

Seriously though, I admire the time and study you have put into it, is that trig or geometry? It's been so long ago. I would be interested in reading a post where you explained this like you were explaining it to someone who mowed grass for a livin'. Thanks Mr. Talbot for pointing out probably what he is talking about.

Josh

 

[Paul Knightley]

There have been a number of odd ideas and theories in the past about tornadoes - they come and go rather like storm season. The last crackpot one I saw claimed that tornadoes come from the sun! Now of course, at a base level they do, as all weather is solar powered...but this claimed that the sun had a direct physical link (i.e. something in the solar wind caused it!).

 

[Dave Van Grun]

If I were a storm chaser, I would first and foremost attempt to realize the extent of the area to be involved. Let's say the May 3, 1999 event were to occur all over again, does that mean that Storms A,B,C,D,E,G,H, and I would reoccur where they did once before? Not necessarily! Chasers who understand mathematics especially teh calculus will have an upper hand because most of what is known about the cardioid comes from calculus: area, length of curve, critical point locations, and so forth. In my opinion, the real work of the national weather service begins with entertaining HOW LARGE AN IMPULSE, WHERE IS THE PRESSURE FIELD RELATIVE TO STRIKE AREA, and so forth! The real truth about the cardioid testifies to tornado families in terms of groups, and large tornado outbreaks in terms of cycles of activity. A chaser will have one-upsmanship on his associates if he knows these things. A tornado outbreak is a dance written on the script of the cardioid and knowing the above will determine how the dance comes off! For example, in the Super outbreak, Storms Depauw, Orleans, and the Fountaintown storm has just happened, where will be the next. Well, the next was Xenia, ninety degrees to the line of the other three and half the distance(from the calculus). It fits the pattern!