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== Mohyi Labs Simplified Vortex Explanation ==
(I'm the inventor of ducted counter vortex radial impeller technology (The Bladeless Drone) and I formulated a more complete explanation of the vortex process for a [https://www.linkedin.com/pulse/climate-engineering-tornados-hurricanes-john-mohyi?trk=prof-post post I made for climate engineering]. Feel free to update the explaination page with the updated explaination and contact me at John@MohyiLabs.Com if you have any questions -John Mohyi)

Climate Engineering: Tornados & Hurricanes

Intro & Disclaimer: 
After researching propulsion in depth, it occurred to me that my understanding of flows for aerospace applications could be applied to natural systems. Below is an explanation of the still poorly understood phenomena of Tornados & Hurricanes consistent within the framework I developed for an advanced propulsion system my team and I have been designing. The explanation below has not been peer reviewed nor has it been subjected to rigorous scientific testing. The explanation below is subject to change, and both support and criticism from experts in the field are welcome as this is meant to spark a conversation. You can also contact me directly at John@MohyiLabs.com or follow [http://www.facebook.com/pg/MohyiLabs Mohyi Labs on Facebook Here].

Mohyi Principle: 
If there is one fundamental truth about the universe, it is that the universe is always seeking balance. Every particle, equation, and person is bound by this fundamental principle, and to understand it is to be a master of fate.

Tornados & Hurricanes: 
Gravity is the primary driving force behind Tornados and Hurricanes. It acts more strongly on denser particles pulling them closer to the center of gravity. Contrary to popular belief, hot air does not rise; rather it is displaced by the colder/denser air that gravity acts upon more strongly. This is the same phenomenon at work when oil and water separate into distinct layers. Gravity attracts the relatively denser water more than the relatively less dense oil. In the process, the water forces the oil to the top. This process in conjunction with the rotation of the earth and thermal expansion/contraction causes wind. The sources of thermal energy are both the sun and the earth itself.

The Vortex begins to form when the denser layer above, relative to gravitational pull, collapses at its weakest point into the less dense layer below, which is usually the center, and the downward momentum has an additive effect. This collapse will take on a concave geometry causing the pressure/density to drop at the center generating a vacuum force as it falls toward the center of gravity.

Every medium is constantly seeking balance or equilibrium. A flow is induced when the balance has tilted. A medium of higher density or concentration relative to its surroundings will always seek a lower state of energy by balancing itself with its environment. A flow in essence is simply an expansion. The expansion, though it expands in all directions simultaneously, will be observed as moving more in the direction of least resistance thus resembling a flow. Equal amounts of energy though are expended in all directions.

The vacuum pressure generated by the collapse of the upper layer into the lower layer will induce a flow from not only above, but from the sides of the vacuum as well. Because of conservation of angular momentum, as the flow converges toward the center of the vacuum it will rotate faster. The vortex will stabilize when the outward rotational force, relative to the center of the vacuum, is in equilibrium with the inward vacuum pressure force within the vortex. Since gravity attracts atoms more strongly closer to the surface of the earth, the gradual increase in the atmospheric pressure gives the vorticity its cone like geometry.

Practical Value: 
The practical value of this model its predictive power, which is a precursor to controlling and harnessing this natural phenomenon. In essence, the power to engage in climate engineering. A few approaches are available some more practical than others:

1) By decreasing the vacuum pressure at the center of the vortex, the vortex equilibrium would expand decreasing the rotation speed resulting from conservation of angular momentum. The most practical method using this approach is to increase the internal pressure via thermal expansion. This may be achieved by focusing a powerful laser at the center of the vortex, or by the use of explosives. This method would only decrease the rotational speed and provide only temporary relief unless the thermal transfer is sustained.

2) By decreasing the density of the upper layer via thermal expansion it is possible to stop a tornado or hurricane before it starts or at least decrease its intensity. This may be achieved by focusing a laser on the clouds or seeding them with an exothermic chemical. This would decrease the density and reduce the gravitational pull. This method may be counterproductive in the long run since the thermal energy will eventually disperse increasing the density.

3) By increasing the density of the upper layer past its collapsing threshold preemptively, it may be possible to prevent or reduce the size of a tornado or hurricane to tolerable levels. A process known as Cloud Seeding is a common practice in China and is used to increase rainfall. By seeding clouds with either silver iodide or dry ice we can fight hurricanes and tornados similar to the way we fight forest fires. (Note: Never seed the central region of an active tornado or hurricane with a cooling agent. That would increase the density and likely exacerbate the problem. You may be able to seed the periphery though.)

4) By building a tower that reaches into the clouds, it is possible to induce a controlled collapse of the denser atmosphere. Once the downward flow generates enough momentum, the gravitational potential energy can be converted into electricity similar to a dam.

Conclusion: 
Climate Engineering is the sensible response to climate change. Both natural and manmade weather fluctuations are a real concern and we have the capability today to respond to these threats.  <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2601:40F:401:180E:A8B8:34A1:D36B:FDAD|2601:40F:401:180E:A8B8:34A1:D36B:FDAD]] ([[User talk:2601:40F:401:180E:A8B8:34A1:D36B:FDAD#top|talk]]) 22:16, 4 February 2017 (UTC)</small> <!--Autosigned by SineBot-->


== Picture of a C-17 Globemaster's vortex ==

Here's a reference to a stunning photograph of a United States Air Force (USAF) C-17 Globemaster III Military Transport's with vortex/twin tornadoes/wake to consider adding to the article:

'''ChamorroBible.org, Fagualo (Octubre) 10, 2004, "Manguaeyayon na Palabran Si Yuus - God's Precious Words, with The Photograph of the Day".''' Photo is in the public domain.  Main site URL: http://ChamorroBible.org (referenced as "ChamorroBible.org" or the "Chamorro Bible" WWW site). 
: http://ChamorroBible.org/gpw/gpw-20041010.htm


On the humorous side see http://forums.fark.com/cgi/fark/comments.pl?IDLink=1160585.

:It is certainly a beautiful photograph. However, I don't think it would add anything to the article, as there are two images here already. Those with broadband tend to forget what loading these pages can be like for poor old dial-up users! [[User:GRAHAMUK|Graham]] 00:11, 7 Dec 2004 (UTC)

== Hopf fibration ==

I was wondering if there are solutions to fluid dynamics equations that "look like" or somehow involve [[Hopf fibration]]s? The Hopf fibration is interesting because it resembles, in many ways, a [[dipole]]. Its vortex-like structure should also be appearant from the picture; I was wondering if there was a deeper connection, beyond the superficial resemblance. For example, is there a [[soliton]]-like solution to eqns of fluid dynamics that resembles the Hopf fibration in some way? Sorry for the "advanced" question, but I am curious. [[User:Linas|linas]] 00:57, 2 July 2006 (UTC)

== "free surface […] is a parabola" ==

I always thought it was a [[catenary]]. Isn't it?
-- [[User:88.134.21.88|88.134.21.88]] 14:36, 5 November 2006 (UTC)

Hmm, well IIRC, the variation in hydrostatic head (proportional to ρg dh/dr), provides the inward acceleration (proportional to ρrω*ω) - so no. [[User:Linuxlad|Linuxlad]] 15:06, 5 November 2006 (UTC)

==  Anyone know why this apparent anomaly? ==

a vortex that involves no shear and so does not require a force to maintain, is called 'forced', whereas a 'free' vortex involves shear so would require some force to keep going.
[[User:Asplace|Asplace]] 01:18, 14 April 2007 (UTC)

:No.  A vortex that involves no shear and so does not require a torque to maintain it is known as a 'free vortex' and velocity is inversely proportional to radius.  A vortex that involves shear and requires a torque to maintain it is a 'forced vortex' and velocity is proportional to radius.  [[User:Dolphin51|Dolphin51]] ([[User talk:Dolphin51|talk]]) 12:42, 22 December 2008 (UTC)

== Confusing examples==
Could someone please clarify these examples, and put them back in the article?
*[[Ice stalactite]]s are formed by a rotating column of downward-moving supercooled brine.
*A small stream of falling water starts rotating immediately on release and does so until the speed of downward movement overcomes the cohesion of surface tension and causes its breakup into spray.  
Thanks... --[[User:Jorge Stolfi|Jorge Stolfi]] ([[User talk:Jorge Stolfi|talk]]) 06:00, 25 September 2012 (UTC)

== The definition doesn't quite fit ==

Just to comment--- reading the definition, it doesn't correlate to the photos provided. The current definition listed here states that a vortex is liquid, when the accompanying photo shows a vortex of gas.  
While I realize that the definition on Wikipedia was probably cut-n-pasted from any one of a half-dozen sites that quote the exact same words, but if you are going to use the image with the airplane, then you must change the definition to reflect this, or get rid of the photo. 
Thanks. [[Special:Contributions/70.188.169.169|70.188.169.169]] ([[User talk:70.188.169.169|talk]]) 06:40, 11 March 2011 (UTC)
:The definition, and most of the article, uses the word '''fluid''', not liquid.  [[Fluid]] is intended to include gases, and a fluid is correctly thought of as either a gas or a liquid.
:I agree that the definition looks amateurish.  It talks about fluid flow that is ''spinning'' and often ''turbulent''.  It also talks about ''closed streamlines''.  I agree that vortex flow can be described as a flow that is ''spinning'', but I disagree that ''turbulent'' is an essential part of vortex flow.  I also disagree that ''closed streamlines'' are an essential part of vortex flow.  For example, when an airfoil is generating [[Lift (force)|lift]] there is a strong vortex at work (called the bound vortex) but the streamlines around the airfoil are not closed.
:My preference would be to define ''vortex flow'' as any flow in which the streamlines are curved lines; and a ''vortex'' as the flow within a boundary where the [[Circulation (fluid dynamics)|circulation]] around the boundary is non-zero.  The popular image of the vortex as a spinning flow with closed streamlines can be described as one excellent example of a vortex, but not the only flow that qualifies as a vortex.  However, I don't have a reference that defines the vortex in these terms.  Can someone help with a reference? [[User:Dolphin51|<span style="color:green;">''Dolphin''</span>]] ''([[User talk:Dolphin51|<span style="color:blue;">t</span>]])'' 04:12, 12 March 2011 (UTC)

== Pictures and descriptions of types of vortex don't match ==
The picture of motion in an irrotational vortex matches the description of the rotational vortex, and visa versa. This is because the faster flow in the center as described in the the free vortex section, causes the leaf points to turn away from the center, whereas the constant angular velocity (omega) with radius described in the forced vortex section keeps the leaf points pointing toward the center. Don't know whether the labels on the pictures or the article sections need to be changed.<span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/ 76.113.109.18| 76.113.109.18]] ([[User talk: 76.113.109.18|talk]]) 02:21, 9 August 2011</span><!-- Template:UnsignedIP2 -->
:Thanks very much for alerting us to this problem.  The problem arose in two edits made on 29 July 2011.  I have now rectified it by reverting to the situation that existed immediately prior to 29 July. [[User:Dolphin51|<span style="color:green;">''Dolphin''</span>]] ''([[User talk:Dolphin51|<span style="color:blue;">t</span>]])'' 22:41, 9 August 2011 (UTC)
Hi, I am unhappy with the gif images of rotating vortexes.  The text states that the rotation of free vortex speeds up as it approaches the center and the image shows something that is not speeding up at all. The ball closer to the center should be going a little quicker. I propose that I or someone else take a video of  stuff suspended in water  going down a plughole to better explain what is happening. In the meantime, does anyone have gif editing software so that we can quickly fix the image?  Thanks, Brian White [[User:Gaiatechnician|Gaiatechnician]] ([[User talk:Gaiatechnician|talk]]) 19:30, 8 January 2012 (UTC)

:The image of the rotational vortex appears to be correct - it shows the body of fluid rotating like a solid, and the two balls rotating through 360° every time the body of fluid makes one turn.  I agree with you that the image of the irrotational vortex is incorrect in that the two balls have the same speed.  As you have explained, the ball on the inner circle should have a faster angular velocity and a faster linear velocity than the ball on the outer circle.  If the two balls were both on the same circle this problem would disappear.  The image of the irrotational vortex is correct in that it shows the two balls having no rotation.
:These two images were added by [[User:Silver Spoon|Silver Spoon]] on 16 Nov 2011.  I will alert Silver Spoon to this discussion and he might be able to quickly fix the situation.
:If you are volunteering to make a video of objects going down a plughole please go ahead! [[User:Dolphin51|<span style="color:green;">''Dolphin''</span>]] ''([[User talk:Dolphin51|<span style="color:blue;">t</span>]])'' 21:35, 8 January 2012 (UTC)
::I see, I could speed up the inner circle, it's no problem to do so :). I suggest 1 turn for the outer equals 2 turns for the inner. {{User:Silver_Spoon/Handtekening}} 10:39, 12 January 2012 (UTC)
:::I've uploaded a new image. When the outer ring makes 1 rotation every subsequent ring makes 1 rotation extra in the same time (that's 2 rotations for the outer ball and 3 rotations for the inner ball in 1 loop of the image. The balls itself don't rotate.) {{User:Silver_Spoon/Handtekening}} 11:22, 12 January 2012 (UTC)
::::That's brilliant!  Thanks Silver Spoon. [[User:Dolphin51|<span style="color:green;">''Dolphin''</span>]] ''([[User talk:Dolphin51|<span style="color:blue;">t</span>]])'' 11:34, 12 January 2012 (UTC)

Actually, the vortex is still not irrotational. Now, the angular velocity is proportional to {{math|6 - {{var|r}}}}, where {{mvar|r}} is the number of the ring from the center, but for it to be irrotational the angular velocity should be proportional to {{math|{{var|r}}{{sup|-2}}}} (compare with [[:File:Vorticity Figure 02 a-m.gif]]). It's a nice illustration though. —[[User:Kri|Kri]] ([[User talk:Kri|talk]]) 14:35, 26 August 2014 (UTC)

:I agree that the illustration currently gives an incorrect rotation profile, with the velocity shown being a straight-line function of radius.  Though Kri, I think it is meant to be proportional to {{math|''r''<sup>–1</sup>}}, surely? I think we really need to insert formulae for the illustrations, with {{math|1={{overline|''ω''}} = ∇ × {{overline|''v''}}}}, with {{math|1={{overline|''v''}} = ''k''(−''y'', ''x'')}} and {{math|1={{overline|''v''}} = ''kr''<sup>−2</sup>(−''y'', ''x'')}} respectively. —[[User_talk:Quondum|Quondum]] 15:18, 27 August 2014 (UTC)

::The velocity should be proportional to {{math|''r''<sup>–1</sup>}}, yes, but the angular velocity should be proportional to {{math|''r''<sup>–2</sup>}}. I agree that it would be a good idea to insert formulae; I recently did the same in the [[Vorticity]] article. —[[User:Kri|Kri]] ([[User talk:Kri|talk]]) 17:11, 27 August 2014 (UTC)

== Role of pressure confusing ==
The way pressure is treated (and also glossed over) is a bit confusing in this article.  Firstly it is stated in the summary that the "the pressure minimum in a free vortex is much lower."  That may be a mathematically precise phrase to use, but in lay speak is an ambiguous way to phrase things, since "lower" can be taken to mean "less intense."  Secondly it is stated that the visible water condensation in a free air vortex is due to the low pressure.  Actually it must be due to low temperature caused by adiabatical cooling of depressurized water vapor, since a low pressure in and of itself without a temperature change would tend to promote vaporization, not inhibit it.  It would be nice if an expression of the pressure gradient were explicit for free and forced gas vortexes. ([[Special:Contributions/71.233.167.118|71.233.167.118]] ([[User talk:71.233.167.118|talk]]) 15:16, 12 August 2012 (UTC))
:Thanks for your comments. I have made some changes - see my [http://en.wikipedia.org/w/index.php?title=Vortex&diff=507142689&oldid=507010085 diff]. Do those changes help?
:The pressure at the center of a forced vortex can be calculated using [[Bernoulli's principle]] and the pressure at some distance from the center. The pressure at the center of a free vortex cannot be calculated because approaching the center of such a vortex the speed increases without bound and is undefined at the center. It is possible to use Bernoulli's principle to calculate the pressure at any point other than the center, and to calculate the rate of change of pressure at any distance from the center. [[User:Dolphin51|<span style="color:green;">''Dolphin''</span>]] ''([[User talk:Dolphin51|<span style="color:blue;">t</span>]])'' 03:29, 13 August 2012 (UTC)

== Redundant pictures deleted ==

With some regret (since they are pretty), I have removed these pictures.  The animated gifs say essentially the same thing but somewhat more clearly. --[[User:Jorge Stolfi|Jorge Stolfi]] ([[User talk:Jorge Stolfi|talk]]) 01:57, 25 September 2012 (UTC)

<center>
{| class="wikitable" style="width:30%;"
|+Types of vortex illustrated by the movement of two autumn leaves
|-
|[[Image:Vortex south.png|227px]]
|[[Image:Free vortex east.png|227px]]
|[[Image:Vortex east.png|217px]]
|-
|Reference position in a counter-clockwise vortex.
|In an ''irrotational'' vortex, the leaves preserve their original orientation while moving counter-clockwise.
|In a ''rotational'' vortex, the leaves rotate with the counter-clockwise flow.
|}
</center>

== Added link to wiktionary, because the plural of vortex is mysterious ==

Nuff said. --[[Special:Contributions/130.85.194.136|130.85.194.136]] ([[User talk:130.85.194.136|talk]]) 19:16, 11 May 2013 (UTC)

== animations ==

Where are the old animations? I prefer them over the new ones even if the overall presentation is better.[[User:Klinfran|Klinfran]] ([[User talk:Klinfran|talk]]) 07:38, 6 November 2013 (UTC)

== Rotational profile ==

[[File:Rotational_vortex.gif|right]]
I think this has to be revised:
"If the fluid rotates like a rigid body – that is, if v increases proportionally to r – a tiny ball carried by the flow would also rotate about its center as if it were part of that rigid body. In this case, \vec \omega is the same everywhere: its direction is parallel to the spin axis, and '''its magnitude is twice the angular velocity of the whole fluid.'''"

It should be the same angular velocity (from current view of picture, i.e.: [[Tidal locking|tidally locked]]), not twice, unless I misunderstand. I also have some doubt about equations and how they have been derived and it would be recommended to refer either to a basic proof or to a reference handbook.--[[User:Almuhammedi|Almuhammedi]] ([[User talk:Almuhammedi|talk]]) 18:36, 7 August 2014 (UTC)

:In the setup of the scenario, the fluid has a specified velocity.  The field of fluid velocities therefore has a curl.  Conceptually, think about the force exerted on the side of the tennis-ball closest to the center of the vortex (in slower moving fluid), and on the far side (in faster moving fluid).  Assuming ideal fluids, and assuming force is proportional to the velocity of the fluid, there is a differential force separated by the diameter of the ball - i.e., a [[torque]].  Conceptually, at least, the ball is expected to start spinning because of this torque.  I'd have to work out the math to see if the net result of this effect on the entire tennis ball yields exactly twice the angular rotation rate of the fluid, but ''conceptually'' this seems correct.  To address that analytically, we'll need to review [[curl (mathematics)]] and set up some equations for the special case of rotational velocity proportional to radius.  Or, we could find and cite a book that works this problem out.  It sounds like a common homework problem.  [[User:Nimur|Nimur]] ([[User talk:Nimur|talk]]) 14:05, 9 August 2014 (UTC)

::The quoted statement is self-contradictory, and has nothing to do with forces (it says "as if it were part of that rigid body"). But even with viscous forces due to relative flow etc., the angular velocity of any (neutrally buoyant) body carried along with the flow would settle to the ''same'' angular velocity as the fluid exhibits. The formula used for vorticity below the figure is incorrect. —[[User_talk:Quondum|Quondum]] 21:52, 9 August 2014 (UTC)

It seems I have introduced an error into the definition of vorticity, and hence removed a factor of 2 that should have been there.  Vorticity is ''not'' defined as the rate of rotation of a small element, e.g. a ball, but as the curl of the flow; this happens to be twice the rotation rate of the fluid element or small ball. I was misled by what was a formula that I removed, so I'll re-introduce the factor. —[[User_talk:Quondum|Quondum]] 04:12, 28 August 2014 (UTC)

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== Confusion as to whether it’s the axis line or fluid that is curved or straight.  ==

The introduction and the summary sections look like they contradict each other in their descriptions of vortexes.  The introduction seems to state that it’s the axis line that can be curved or straight, whereas in the summary it seems to state that it’s the fluid that can be curved or straight. So which is it, the fluid or the axis line? Btw, the summary could really use some proofreading for grammatical and syntactical errors. [[User:Alialiac|Alialiac]] ([[User talk:Alialiac|talk]]) 20:58, 9 August 2018 (UTC)

== Merge ==

See discussion under [[Eddy (fluid dynamics)]] [[User:Biggerj1|Biggerj1]] ([[User talk:Biggerj1|talk]]) 17:17, 19 June 2022 (UTC)
: {{done}} see discussion there. [[User:Biggerj1|Biggerj1]] ([[User talk:Biggerj1|talk]]) 08:48, 17 July 2022 (UTC)