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Navier-Stokes Excistence and smoothness problem doesn't have solution. The physical premises of this mathematical problem is not correctly understood. Turbulence is a "crack" on fluid; Internal surfaces inside the fluid. It's Collision and friction, not viscous forces.
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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,
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;
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
Cover Letter
Jouni Jokela
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.
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]
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
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
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 cant be created nor lost.
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
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ResearchGate has not been able to resolve any citations for this publication.
After model testing, a number of Minimum Energy structures have been built and have been subjected to flows of some magnitude during the reasonably wet summer of 1970-1971. It is proposed to give the detail design of some of these structures and a report of their observed behaviour. As the design procedure is not restricted to road structures, the behaviour of other structures is also reported as their performance is essentially linked to the validity of the basic concept. It would appear that the concept of constant total energy and compatible specific energy is valid within the limits required for practical design. That the minimum energy condition can be used to provide economic structures for a wide variety of purposes. Although the concept leads to, quite different forms which for full development may require some variation of traditional construction requirements, it has been shown that with present methods considerable savings are nevertheless possible. The concept offers practical solutions to ,previously unsolved problems. The design techniques suggested to make use of this concept allow for much more detailed analysis than is otherwise possible. Essentially the designs minimize the r3ndom turbulence normally associated with Civil Engineering structures. Although the design determines wher e energy is .bes t dissipated, it is still not possible to control "lith any accuracy the rate of dissipation. The limits to which the techniques can be successfully used are not yet defined, but the operation full size does appear to be more favourable than on a model.
The book is an introduction to the hydraulics of open channel flows. The material is designed for undergraduate students in Civil, Environmental and Hydraulic Engineering. It will be assumed that the students have had an introductory course in fluid mechanics and that they are familiar with the basic principles of fluid mechanics : continuity, momentum, energy and Bernoulli principles. The book will first develop the basic principles of fluid mechanics with applications to open channels. Open channel flow calculations are more complicated than pipe flow calculations because the location of the free-surface is often unknown 'a priori' (i.e. beforehand). Later the students are introduced to the basic concepts of sediment transport and hydraulic modelling (physical and numerical models). At the end of the course, the design of hydraulic structures is introduced. The book is designed to bring a basic understanding of the hydraulics of rivers, waterways and man-made canals (e.g. Plates a-1 to a-13) to the reader. The lecture material is divided into four parts of increasing complexity : - Part I : Introduction to the basic principles. Application of the fundamental fluid mechanics principles to open channels. Emphasis on the application of the Bernoulli principle and Momentum equation to open channel flows. - Part II : Introduction to sediment transport in open channels. Basic definitions followed by simple applications. Occurrence of sediment motion in open channels. Calculations of sediment transport rate. Interactions between the sediment motion and the fluid motion. - Part III : Modelling open channel flows. Physical modelling of open channel flows. Numerical modelling of open channel flows. Physical modelling : application of the basic principles of similitude and dimensional analysis to open channels. Numerical modelling : numerical integration of the energy equation; one-dimensional flow modelling. - Part IV : Introduction to the design of hydraulic structures for the storage and conveyance of water. Hydraulic design of dams, weirs and spillways. Design of drops and cascades. Hydraulic design of culverts : standard box culverts and minimum energy loss culvert. Basic introduction to professional design of hydraulic structures. Application of the basic principles to real design situations. Analysis of complete systems. Applications, tutorials and exercises are grouped into four categories : applications within the main text to illustrate the basic lecture material, exercises for each chapter within each section, revision exercises using knowledge gained in several chapters within one section, and major assignments (i.e. problems) involving expertise gained in several sections : e.g., typically section I and one or two other sections. In the lecture material, complete and detailed solutions of the applications are given. Numerical solutions of some exercises, revision exercises and problems are available on the Internet (Publisher's site : A suggestion/correction form is placed at the end of the book. Comments, suggestions and critic are welcome and they will be helpful to improve the quality of the book. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. "Errare Humanum Est" .
  • Ven Te Chow
Ven Te Chow, Open Channel hydraulics, 1959, page 8.