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Elsevier Editorial System(tm) for Annals of Physics

Manuscript Draft

Manuscript Number:

Title: Turbulence

Article Type: Research Paper

Section/Category: Other

Keywords: Turbulence; Continuity

Corresponding Author: Mr. Jouni Jokela,

Corresponding Author's Institution:

First Author: Jouni Jokela

Order of Authors: Jouni Jokela

Abstract: ABSTRACT

Turbulence is characterised by irregularity, diffusivity, rotationality and dissipation. It's said to be the

most important unsolved problem of classical physics. Maybe the answer is just too simple; if

Turbulence is just fluid broken in parts? Just like one solid obstacle holds it's movement compared to

the many solids which collides and starts to move all directions.

This paper tries to conclude my observations about the issue so far. It should be said loud, already here

at the very beginning. That though Reynolds number and different roughness coefficients are widely

used, there still isn't any theorem relating to their explanation. They are only based in experience. And

of course, the centuries of experience do make them quite accurate. But they are unable to explain

Turbulence completely. The idea and knowledge about the issues is gathered through my experience

and work done with Open channel flows, my own hydro turbine development, Injection works and

plastic-elastic expansions joints. So I am trying to explain this through the only way I can; through my

own life experience.

Annals Of Physics, Cover Letter,

10.2.2015

Dear Editors,

Tomorrow I am 40. And my life hasn’t been anything “concentional” so far. And I’ve been quite a

successful in my doings. So, though I am just a simple “civil engineer”, I’ve surely recognized that I

am in a level way above that.

This paper holds somehow new thoughts about Turbulence. And I’ve had this idea for few years

already. And I’ve been working in areas which simply provide the practical experience needed to

create these thoughts. So, it’s obvious to me, that this paper might not fill your conventional

requirements. I do not know i.e. any particular Reviewers for this work. But I’ve been trying to

speak with so many professors already about this, that I should have got some rejection. So far, the

only answers I’ve got are “interesting” or no answer. So please don’t let that disturb you too much.

I’ve collected also a quite amount of data. But the basic idea is really simple to see by just simply

boiling some water and mixing it. I attach few fotos about this, where you might see it with your

own eyes. But the best way to catch this is a video. And I do have video’s in my youtube channel

about this issue. I even did a new one cause this paper; with distilled water, and arranged lights and

everything. But if the picture quality doesn’t fit, you can’t see too much. Here’s a direct link;

https://www.youtube.com/watch?v=PN6gJq8JISU

So, please sit down, and think about this your self. I mean it might really be so simple?

Best Regs,

Jouni Jokela

Aussenmatteweg 22

CH-3714 Frutigen

+41 79 265 4043

+41 33 534 3064

jouni@jokela-turbine.ch

https://www.youtube.com/user/JokelaTurbine

Cover Letter

Turbulence

Jouni Jokela

jouni@jokela-turbine.ch

ABSTRACT

Turbulence is characterised by irregularity, diffusivity, rotationality and dissipation. It’s

said to be the most important unsolved problem of classical physics. Maybe the answer is

just too simple; if Turbulence is just fluid broken in parts? Just like one solid obstacle holds

it’s movement compared to the many solids which collides and starts to move all directions.

This paper tries to conclude my observations about the issue so far. It should be said loud,

already here at the very beginning. That though Reynolds number and different roughness

coefficients are widely used, there still isn’t any theorem relating to their explanation. They

are only based in experience. And of course, the centuries of experience do make them

quite accurate. But they are unable to explain Turbulence completely. The idea and

knowledge about the issues is gathered through my experience and work done with Open

channel flows, my own hydro turbine development, Injection works and plastic-elastic

expansions joints. So I am trying to explain this through the only way I can; through my

own life experience.

Continuity Problem

There are few hints I’ve found from literature which guides to this direction. The paper

from Gordon McKay[1], and the book of Hubert Chanson [2]. Both state clearly that the

form losses are the major cause for energy losses. And as the turbulence is the major cause

for energy loss, thus from change is also the major cause for turbulence. Yet, if the form

change is streamlined in a matter where the continuity rules are hold, then no turbulence

might occur no matter how high the velocity is. And thus the only cause for turbulence is

the sudden changes in velocity or pressure; problems in continuity.

These continuity problems can be easily understood in everyday life. It’s not the travelling

speed which is dangerous. It’s the sudden stop which kills, if you face a traffic accident.

TURBULENCE

One of the questions which had leaded me to this answer is; why the efficiency of high

specific-speed turbines actually drops in low heads? The reason is of course the mixing

work, which proportion grows bigger and bigger. By developing this turbine of mine, I

noticed that the definition of Turbulence is still incomplete. Its characteristics are defined as

“chaotic, mixing, rotational and energy dissipation”. There is i.e. Reynolds number or

Navier-Stokes equation, which tries to explain this. There is even a Mathematical problem

called “Navier-Stokes existence and smoothness” which assumes, that this all could be

explained and solved mathematically. But it can’t be done. There is no solution. Because

the physical background of the problem is not correctly defined.

While developing this whole hydropower concept of mine, I also needed to optimize all the

details outside the turbine, as hydro power plant always starts from an open channel flow,

and ends to an open channel flow. In the open channel the Turbulence can be simplified to

two dimensional eddies. And also in open channel the continuity can been used efficiently

to minimize the energy losses. And these led me to notice this old paper from Gordon

McKay.[1] It’s the only paper from this art, which clearly states that fixing Turbulence and

velocity with a causality “must be grossly in error”. Though they do correlate, there is no

causality. Reynolds number speaks about this Correlation, and there truly is statistically

remarkable dependence. But there is no Causality. This can be verified from many sources,

i.e. Ven Te Chow states clearly that flow can be laminar with Reynolds number “as high as

50 000”, and “It should be noted that there actually is no definite upper limit”. [3]

*Manuscript

Click here to view linked References

So if turbulence is not connected in velocity, what is it? A hint can be found from a 2D

field; there the vortex forms a relatively simple minimal surface pattern, shown in figure 1.

Blue/cyan lines describe the rolling parabolas. Black lines describes the axis along the

parabola is rolled, and also to destination of the green line and the end of green line

describes the focus of the blue parabola, which follows the red curvature forming a

catenary. The size of the pattern must then slightly grow just to fulfil the continuum laws

(yellow lines); the vortex centre rotates as the end result of the rolling parabola, and these

rotations are then forcing the fluid to move perpendicular to the original flow direction. But

as there are always two similar flows on counter directions, (Simply must be, according to

Newton) this doesn’t of course increase the volume/width of the pattern, it is the change on

temperature, what does it. Note, that all these Parabolas and catenaries are drawn with the

same parameters. Only their positions are slightly corrected as can been noted from black &

yellow lines. It is also to been noted, that the parabola defines also the interval of the

eddies.

The velocity and the pressure profile of a vortex forms a minimal surface. In 2D field it is a

catenary. I.e. a soap bubble is a minimal surface. -> Surface! The water has surfaces in it.

The Turbulence is a nothing else but the water cut to a many fluid components having their

own surfaces. And these surfaces slides against each other giving a relief compared to

viscous forces which causes the rotational movement. (Rotation characteristic) This

molecular cut in fluid aloud increased convection through the fluid, i.e. aeration in white

waters. And the increased surface amount makes also the chemical dissolution very

efficient. (Mixing characteristic) Cutting the existing fluid, and creating more surface

having surface tension is also very energy consuming it self; with water, the Surface energy

is 0.072 J/m2 (Energy dissipation characteristic). This energy can not be returned to

pressure or velocity, so when these eddies disappear, it must be transferred to heat. It should

be also noted, that all surfaces has a friction. And thus some part of velocity forces is still

transferred over the surface. And of course also the pressure is transferred completely

through. But with surfaces the pressure just causes these fluids to re-shape, deformate with

very irregular-seeming ways. Exactly like many solids colliding together in an explosion or

so. This all makes it very difficult to notice the difference between viscous forces and

forces; like friction, pressure, going over surfaces. But the Newton’s laws remain

completely valid. The collision angles of these elastic surfaces just gives so many options.

Figure 1: Karman vortex-street, rolling parabolas(Cyan) and Catenaries (Red)

Navier-Stokes existence and smoothness problem

The further conclusion which can be drawn from all this above, is, that the premises of this

mathematical problem are wrong. As there is not only one three dimensional volume, but a

volume which is divided by their own surfaces to many different volumes, which can’t

continuously transfer velocity and pressure over their own surface’s, so the three

dimensional flow will finally always become to it’s topological limits and must thus

explode. This is not the case in 2D field, where the vortex surfaces are more able to transfer

the velocity and pressure over their perpendicular surfaces. Shortly, continuity is not

possible over the surface, but only collision kind of forces can be transferred. This makes

the turbulence flow really chaotic; as the collisions are of course dependable on the surface

and collision angles. And these are highly variable in case of fluids.

Simple calculation about the water splitting energy

If a laminar flow is cut to a typical drop size; 0.05 ml = 50 mm3 cubic-shaped drops

assumed, the surface energy consumed by a 1 m3 of water is 270 x 270 x 270 drops, each

with a 81 mm2 surface, totalling 1628 m2, 0.072 J/m2 each, sums up 117 J, Which already

makes a head loss of a 1.2 cm. If the splitting is made with a sudden pressure shock, the

drop size will of course be much smaller, and the surface amount exponentially higher, A

head loss of 1 m, needs actually only that the water is split to a particle size of 132 m2/kg

(Blaine fineness), and though that might sound much, i.e. a normal Cement has typically

500 m2/kg, and Micro-cements over 1200 m2/kg.

This calculation example doesn’t even include the energy losses caused by the viscous

losses in the rotating vortices of the turbulent flow. This all concludes the great importance

of holding the continuity and avoiding all kind of flow disturbances. In open channel flows,

the form losses could count up to 92% of the total loss, so the meaning of surface roughness

can be only 8 % of the losses. [2]

Combining Chemistry and Physics.

If we look the chemical bonds of atoms? And atoms are simplified as spheres. And these

speheres has radius; ie. Wan der waals radius, or Covalent radius. Well, I must admit I

don’t know too much about these, but I don’t let that to prevent me calculating. And In try

to keep this calculation simple. So I choose oxygen, as its Chrystal structure is cubic.

Maybe we can find a simple causality of the physical properties of a single atom and the

physical properties of a mass of these atoms.

Oxygen; Wan der Waals radius; 152x10^-12 m, 152 pm

O2 forms a double sphere, with 120 degrees contact angle.

volume of this double sphere; 2.482302343x10^-29 m3

Density of liquid O2 at b.p. 1.141 g/cm3

Molare mass; 16 g/mol

Volume of a mol calculated from this double spehere;

1.494877x10^-5 m3 /mol

or 14.94877 cm3/mol

Density of this double sphere volume calculated through molare mass;

16 g/mol / 14.94877 cm3/mol = 1.070 g /cm3

Difference 1.141/1.07 is moderate; only 6.6%

Turbulence and Froude number. Minimum Energy Loss-Structures

MEL-structures were invented by Gordon McKay in 1959. They are designed simply by the

continuity rules, which amazingly also results the Minimum Energy Loss conditions. The

continuity is hold by calculating the constant total head, also constant total Energy amount.

The flow conditions are optimized by Froude-number. The form changes are streamlined

very similarly like in Venturi-tube. The pressure change is corrected with Elevation change.

This aloud use of higher flow velocities and smaller cross-sections. The velocity is created

with lower water surface level and river bed. This provides very economical Culverts.

Also MEL-Weirs have been made. They are basically overflow embankments, and they are

beneficial as they allow an additional water to be stored in the reservoir without flood

problems. These Mel-Weirs are not dissipating energy. Their purpose is to conserve the

energy and to make the downstream flow velocity higher and thus also the flood-flow

capacity higher.

It should be noted, that the though the Froude-number correlates perfectly with the flow

condition and the energy losses, it doesn’t even need to be one. As long as it’s kept below

FR=√3=1.73, and the changes are streamlined, the energy losses remains negligible, as

shown in Figure 2. [4]

The reason why the Froude number √3 is the limit where the turbulence called “hydraulic

jump” begins in open channel flow at that point, can also been read from this figure above.

It’s the point where the flow depth doubles from 0.4 to 0.8 over the hydraulic jump. Shortly

said it simply supports perfectly my theory about Turbulence. I mostly think this through

small balls, and with one ball you can’t push more then two balls wide at front of you, as

the two balls in front will split apart at the point where the ball behind them is pushed

between them, which must lead to a flow separation, -> Turbulence.

Here is a certain analogy to Betz law. Here the flow is 2D though, and in Betz law the flow

is 3D. This makes the possible velocity change ratio to v1 / v2 from 1/3 in 3D to ½ in 2D.

The analogy is of course the question about the kinetic energy; if you lower the velocity too

much, then you’ll have disturbing stand still, a blockade.

It should be noted, that this also explains the reason for the flow undulations. If you

calculate the continuity of the energy to FR =1.73 and then over the hydraulic jump

doubling the depth, you really half the velocity. But the total energy is not correct! As there

are no particular losses, the y2/E1 just doesn’t fit;

0.6 velocity head gives a √(0.6*2g) = 3.43, and the jump from 0.4 -> 0.8 half’s the velocity.

So the velocity should be 1.72. But the velocity head of 0.2 gives √(0.2*2g) = 1.98! So

there is no solution. Other vice said, this velocity of 1.72 gives a velocity head of 1.72^2/2g

= 0.15, which must be the average velocity head of the flow according to the continuity. So

the velocity will be 1.72, but there must be waves to make the average velocity head to

meet this velocity; I should be calculated more carefully and tested with experiments, but I

simply expect these waves to be from 0.1-0.2 of this energy head.

But again; as long as the fluid is not split in parts, no turbulence is necessary to occur, and

no energy losses must happen, –As It’s clearly verified with this USBR experimental curve.

It should not be forgot, that Froude Number still defines the optimal flow condition. And

immediately when we go over Fr=1, the flow will starts to separate near the surface. As

long as the velocity accelerates, this just doesn’t cause turbulence, but once this

Figure 2: USBR-experimental curve,

acceleration ends, there will be disturbances developing near the surface, and these

disturbances will finally disturb the whole flow; “fully developed Turbulence”. Shortly,

Below FR=1, the channel surface has practically no influence to the flow, as long as the

continuity is not disturbed. Between FR=1 and FR=√3 the surface has influence to the

development of the turbulence. And above FR=√3, the flow conditions can be completely

destroyed by any downstream disturbance independent from the channel surface quality.

A comparison to Mechanical equilibrium can be made;

FR<1 Stable equilibria.

FR= 1 to √3 Neutral equilibria.

FR>√3 Unstable equilibria

Conclusions

Mass is energy, or everything is finally just energy. And higher energy needs, and takes

more space. Space is time. And all the energies drag each other like love. An issue, I do not

know too much. I’ve just been dragged to all directions through my life.

But I do see causality between surface tension, Turbulence, atomic structure and the

energies needed to vaporize or melt material. I hope some one can help me with these

thoughts, though it doesn’t really matter. Cause it just doesn’t seem to make too much of a

difference, if we understand more or less. There will always be people claiming that you

need to pay some taxes to save the world or pardoning your sins.

Though, Energy can be neither created nor be destroyed, it can only change its form, it can

just be redefined in higher or lower forms. But it can’t be created nor lost.

Acknowledgements

I am about to send this paper to Annals of Physics, and the claim that I have to mention all

organizations who have funded my research. Well. The answer is; none, -Nobody.

I’ve had the opportunity to use the ITF Lab of FHNW Windisch; opportunity I am grateful

for. But then, I’ve paid for that, the price which was asked.

This paper holds my first properly published, somehow complete view about the continuity

and Turbulence. I’ve had this idea for a long time. I tried to publish this Figure 3, in

“Annals of Physics” at October 2012, but my one A4 paper was found not to be fulfilling

the requirements given for such a scientifical-paper. I shared this same paper and idea with

Hubert Chanson already at that time. And as I thanked him then, I want thank him again for

these words “Interesting, original, not conventional” -he replied me. Actually they are the

only supporting words so far, which I’ve had without need to fight against some prior

assumptions during the struggle I’ve had with these developments.

As I’ve also read the Book of Mr. Chanson, and I must share the comment of Canadian

Journal of Civil Engineering about him; “Reading through the book, one cannot miss the

tremendous enthusiasm the author has for hydraulic engineering.”

But most of all, I want to thank “CH”, an energy source which has provided myself the

energy and tremendous enthusiasm I needed myself to take these final steps forward and

say loud these unconventional thoughts of mine. I think I have now used this energy the

best way I can, and I would be happy to give it back somehow, -naturally redefined.

Jouni Jokela, Frutigen, Switzerland 10.2.2015

References / Data sources

[1] G.R. McKay, Design of minimum energy culverts. Oct. 1971, Introduction, page 1.

[2] H. Chanson, The Hydraulics of Open Channel flow: An Introduction, 2004, page 228.

[3] Ven Te Chow, Open Channel hydraulics, 1959, page 8.

[4] Ven Te Chow, Open Channel hydraulics, 1959, page 397, Fig 15-3

Video material is available on youtube-channel www.youtube.com/user/JokelaTurbine