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Author Topic: Fractal foundation of Fluid Mechanics  (Read 40041 times)
Description: Discussion.insights, notions and paradigm shifts
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jehovajah
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« Reply #30 on: July 27, 2013, 11:32:46 AM »



This is a part of a much larger sculpture designed to explore diffraction and interference patterns in a fluid medium. The image shows a region where vortex shedding is evident .

At the same time, this vortex shedding is interpretable as interference patterning during diffraction.

Fluid dynamics really has it all covered!

Best of all it is Fractal.
http://jehovajah.wordpress.com/jehovajah/blog/2013/07/27/single-slit-interference
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #31 on: August 10, 2013, 02:44:43 PM »

I posit that trochoids of the sphere are general solutions to the Navier Stokes and Euler equations for fluid mechanics

http://jehovajah.wordpress.com/jehovajah/blog/?id=60182732

But I have much to do to recommend the idea.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #32 on: September 18, 2013, 03:35:09 PM »

A solid has 6 degrees of freedom but a limitless set of axes of rotation.

A fluid has n degrees of freedom as well and a limitless set of axes of rotation. It is the near solid or fixed relationship between these degrees of freedom in rotation that is usually studied. The surprising fact is that rotating frames of reference self organise!
<a href="http://www.youtube.com/v/Ans3tnvMyTk&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Ans3tnvMyTk&rel=1&fs=1&hd=1</a>
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #33 on: October 08, 2013, 11:54:43 AM »

So now i am pretty much comfortable with the notion of Aether and Ether.

Philosophically it is unavoidable, the science that denies it is Luddite. The fact is the mathematics is derived based on its assumed or implied existence, and it is merely blinkered thinking to insist that the mathematics is sufficient to describe what in fact we require philosophy to do.

Somewhere in the early 20th century huge propaganda machines warped our natural philosophical understanding of the experience of reality, for mainly national security reasons. Then scientists found that this se of affairs was a cash cow for research funding, and no one really wanted to change it! do not rock the boat!

The Newtonian fluid motive is my starting point. To it i must add a notion due to Dirac and Newton, the notion of an Impulsive force. The Dirac delta function is the mathematical model of an impulse, and what we have to observe is that an impulse is an instantaneous force effect. the notion of instantaneity does not rely on time, In fact time is problematic. Instantaneity depend on differentials of motion, From the differentials of motion we necessarily must expect a motion transmission .

Because there is no real notion of time , we must expect that motion is fundamental to the reality in which we have our experiences. Thus if i apprehend a motion, i know from experience that motion will continue in some fashion. The fashion of this motion is varied and complx and fractal, but we can "rationalise " it. When we do the ratios of experiences of motion we define this ratio experience as time!

Tyme, the old word from which time is derived meant the records of positions in space. The modern notion of time retains that idea fundamentally. Time is the position of some hand on a clock face, the position of some digital represetation in a sequence, the postion of some pensulum in som sequence of periodic motions etc.

The point is that time represents the position of some specified indicator in its inherent motion. Instantaneous therefore refers to that position in its motion if we could take a picture of it on a very fast film, in a movie. Each frame would capture an " instantaneous position".
The fact that some logicians might confuse themselves by discounting the term instantaneous, or confusing motion with the existence of time need not concern us. Logically motion must be fundamental, Without it nothing would move!

So now the instantaneous motion or displacement we have a tool to measure, say Hooke's spring force measure, must lead us to expect the motion to continue. This motion continuing is what we call strain transmission. What Newton attempted to get us to focus on was not continupus motion, but continuous rest, or uniform motion. These phenomenon reveal that forces are in equal and opposite action, in a space or sphere of equilibrium, called inertia, so that motion is kept in a dynamic equilibrium, or returned to a dynamic equilibrium by these inertial forces.

The consequence of this is that motion in space is not only endemic, but it is in a kind of dance that attempts to restore a notion of equilibrium, or inertia. Inertia in this sense is a local phenomenon, and Newton concluded it was relaed to density in space. His vision of space as a unierse was that it was not uniform in density. What he could not grasp was how that density varied. In particular, in a rarefied atmosphere how could force be transmitted?

We must be aware of the great sophistication of Newton and La Sage. The notion of a wind was not inimical to their thinking. For a great while Newton, in correspondence with La Sage felt that a corpuscular wind might be the transmitter of force, much like the way the wind blows the sale of a ship. However, this explanation came very close but failed to give a consistent explanation. Newtons own work on Fluyid mechanics gave him the same hopelessly complex situation which he could not resolve.

The resolution was universally thought of as being the field concept of Faraday, and Maxwell. However this was not the case! The real solution is the correct notion of motion and the Diract delta function. 
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #34 on: November 16, 2013, 12:52:29 AM »

<a href="http://www.youtube.com/v/6MstJEAlNFs&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/6MstJEAlNFs&rel=1&fs=1&hd=1</a>

These are the equations I will modify to describe fluid dynamics with shock waves described as Dirac delta functions.

The general pressure bubbles will be modelled by trochoidal type equations of these forms.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #35 on: December 31, 2013, 10:30:04 AM »

I have been busy grasping at straws.

Fluid mechanics is such a deep paradigm that i have too many things to declutter from to grasp its essential simplicity.
Initially fluid mechanics was a means to an end: to understand electrostatics and magnetostatic in terms of the Shunya field, the field whose spaciometry is the vortex and whose trigonometry is the roots of unity and the zeroes of space.

``it has taken me a while to be able to formulate it in language in this fashion, and it is poetry that is more meaningful to me than the reader, i suspect.

So again i recommend the amazing app by Lazarus Plath here
http://home.comcast.net/~trochoid/TroWithMesh.html
for you to explore in your browser running java script.

Once i thought i understood more than his ineffable explanations at youtube qqazxxws, but i realised pretty early on i did not have the insight that he intuits in a way he finds hard to explain.

Play around with clicking and dragging. click on the numeral boxes and drag. click under or over the numerals. Click the tiny boxes in the top left. Explore.

this app is based on what i call Twistors. only radius and rotational frequency are used. everything is displayed by radius and relative rotational frequency.
Meditate on that, and how 2 dimensions rotated relative to each other in the screen plane ostensibly can develop a rich affine geometry/ spaciometry.

Think as Grassamnn thought, particularly about Phorometry.

This is why Newton could only go so far in his fluid dynamics, and why he came closest to understanding action at a distance.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #36 on: January 31, 2014, 08:32:53 PM »

Claes Johnson on fluid dynamics

<a href="http://www.youtube.com/v/t7e_6bkUFzE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/t7e_6bkUFzE&rel=1&fs=1&hd=1</a>

And on D'Alembert paradox.

<a href="http://www.youtube.com/v/3u3OzSlEvdk&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/3u3OzSlEvdk&rel=1&fs=1&hd=1</a>
Johnson and Hoffman solved the paradox but did anyone care?
« Last Edit: January 31, 2014, 08:57:10 PM by jehovajah » Logged

May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #37 on: February 01, 2014, 01:24:59 AM »

This article on resonance is particularly interesting for fluid mechanics.
http://en.wikipedia.org/wiki/Self-resonant_frequency

It is known that Freak waves appear in the open ocean unexpectedly. What is not known generally is that marine scientists used to cow tow to a theoretical model which said they were impossible! Thus resonance in fluid systems was denied by ignorance ?
http://www.ivorcatt.co.uk/x3cj.htm
This reticle by Ivor Catt shows how this ignorance extends into the " electric" realm, in terms of the notion of self resonance.

Self resonance seems to be an oxymoron. An object that vibrates clearly vibrates with itself! Resonance is where another object vibrates in sympathy with another or when a vibrating object shows marked and distinct amplitudes in its vibration.

In the mantra of sine waves this is when waves constructively or destructively interfere. This happens because " waves" pass through each other and interfere with each others wave motion.

Thus we can refer to interference patterning when we are discussing Resonance, but we must not confuse the sine wave model with physical wave processes.

Self resonance can only refer to physical vibrations within a bound form reflectively interfering with each other. Unless reflection occurs there can be no self resonance.

Ivor's articles states that a capacitor has no self resonant frequency for in series capacitance.  If there is no undulation or vibration then there can be no interference pattern. However. A reflective plane wave must aggregate additively in this case, so I would expect the capacitance to increase over time.

Thus the charging of a capacitor is the interference behaviour of a plane or step wave in this case.

Ivor mentions that self resonance exists in an inductor. This means tht magnetic flux within an inductor oscillates or undulates. The variation in magnetic flux kin an inductor may itself be due to the variation in the energy pumped around an inductor, ie an AC induced melectromagnetism. In this case , there is no reflection, but hysteresis provides the variation in the magnetic flux behaviour, and so the inductor exhibits resonance , but not self resonance in terms of reflection. This would be induced or driven resonance.
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jehovajah
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« Reply #38 on: February 01, 2014, 08:32:46 AM »

As far as physical waves go, I have previously mentioned the strain ellipsoid and how that gave me a notion of a pressure bubble, I also mentioned my experience of physical waves on the beach and their cylindrical rolling action, and how they seem to roll onto the beach at an angle while collapsing into foam.

Looking out to sea I noticed the characteristic undulatory appearance and dynamics, and of course an extended ellipsoid fits the image better than a extended cylinder. The dynamics is like beer barrels rolling over each other! Stacked logs come to mind, but they are too cylindrical.

Smooth pebbles might be another physical sample especially as they are tipped out of a dumper lorry. Any rockslide has the same characteristics and in fact scientists have expressed surprise at how fluid the motion of rolling rocks appears when seen on films of landslides or rock avalanches. Snow avalanches, once they begin to break up into rolling chunks have the same motions.

However the ellipsoid is just one physical form that fits the bill because we have studied it very well. The other Shunyasutras I will refer to as trochoidal forms and these have a sea shell like form or appearance. A special such form involves trochoidal space curves called Loxodromes and these are particularly significant for descriptions of electro Thermo magneto complexes as wave foms.

In this regard the simple helical space curve considered as a wave rolling perpendicular to its central axis may be a sufficient model for an extremely long ellipsoidal or loxodromic rolling physical wave.

The sine wave model has really obscured the physical wave models, and in particular, the propagation of energy in a physical wave.

For instance: the wave that attaches itself to a conductor is such a long rolling wave. It rolls onto the conductor from the surrounding "dielectric" by means of magnetic coupling. The energy transfer along the conductor is in the space around the conductor and it progresses along the surface of the conductor as a wave coupling action. Think of a sea wave rolling onto the beach . The wave engages the shore line as it is , not as a straight line, consequently the foam takes on n undulatory form relative to the shore line. Similarly, as the approaching wave from the dielectric is magnetically coupled to the conductor a sharp rise time is seen as it progressively attaches. This rise time travels at the speed of light as a pulse front along a magnetic ' shore line'.

The discussion of how a cell battery or a capacitor battery achieves or is involved in this I will leave to another time, but it involves twistors and Twistorque.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #39 on: February 01, 2014, 11:14:59 PM »

The secret of flight is such a simple breakthrough it deserves pondering

http://secretofflight.wordpress.com/

Essentially density is the key.

The concept of density enwraps gravity and levity into one misunderstood concept! We measure gravity by levity and levity by gravity, and say that the denser object is a multiple of the density of the lighter or less dense object. And we imagine force moments rotating against each other. The levitating force in the beam is ignored, the levitating force in the environment is ignored. It is only when a balloon lifts that we recognise it. Then we mis ascribe it. Density pushes against its environmental density. It does so through surface area. Density is another example of Newtonian fluid motive or energy. And the first transformation of energy is into density force within a volume with a surface area.. As that surface area increases that density force spreads out to act on more of its environment

The greater surface a density force acts through the more levity it exhibits .

When the environment acts on a surface the density force is crucial to levity. By compressing the environmental density force into a smaller volume levity is induced in the wing which being rigid maintains it's density force

The environment above an aerofoil does not compress, instead it works to move out of the way . Consequently it does not impinge its density force on the aerofoil.the net density force of the aerofoil helps spread the environment out above the wing. Finally, at the trailing edge the disturbances generate vortex columns in the environment. These vortices have no net density force because it is applied in a spinning vortex. This allows increasing environmental energy to be stored in the vortices but means the leading edge of the aerofoil is applying density force to generate work on the environment that results in the vortices, and the compressed environment is reacting with density impulse force, creating levity and drag.

Drag is levity applied in a direction other than up.

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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #40 on: February 08, 2014, 09:50:18 AM »

Fluid mechanics from an artists point of view!



My most impressive work on the subject fluid mechanics, but a very bad photo.





Further pictures can be found through the following links:
http://www.wackerart.de/gallery/creation.html
http://www.wackerart.de/gallery/gravitation.html

The following photo gives a better impression of the picture firewall and some other works of mine as has been presented on the exhebition art and physics in 2009 in Merane.




Hermann
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jehovajah
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« Reply #41 on: February 09, 2014, 12:46:40 AM »

Thanks Hermann! Some great impressions!
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #42 on: February 09, 2014, 01:43:33 AM »

My research into barycentres has thrown up some new insights.

While the aether was a common religious concept borrowed by theosophers in their philosophical attempts to describe the workings of the material world, interdpfaced with a spiritual world. Philosophers were not do keen. In fact they often avoided using the term, which was becoming a catch all.

Descartes popularised its fundamental mechanical use as a medium of extension within the spirit enfused reality ordained by god. He ran into trouble with those who believed in transsubstantuation, because god to them could not in any way be physical, or have physical properties!

Leaving their ideas to one side we find the aether taking on a kind of strain or active medium role. Although the term Plenum is not strictly the same as the aether, by the time of Grimaldi and Huygens, the plenum was generally confused with any number of ideas of an aether.

The more mathematical and geometrical philosophers tended to keep clear of too close an association with any particular concept and instead focused on mathematical or geometrical laws or uses of resistance go motion.

The mechanics of Archimedes and Timaeus had passed down through the Arabic scholars to the west. By that time the geometry of the mechanical systems had been extracted and in this guise geometrically examined and improved.  The Geometers of the west tended to despise mechanics, Leonard's Da Vinci bing a noteable exception. Consequently many confused geometry with Euclidesn Pythagorean teachings, which were also extracted from the mechanics of the ancient civilisations.

It should therefore be no surprise that geometrical forms measure mechanical and physical motions, energies and forces, What was difficult and not easily studied was the dynamics of fluids.

It really did have to wait until Archimedes to make that Eureka discovery, that volume and density of liquids were related to flotation in a measurable way.

Newton's notion of density girs straight back to Archimedes formulation.

In his work on fluids Newton as was common characterised it as a resistive medium, rather than an elastic one. Elasticity was the boundary between a fluid and a corpuscular body! Thus fluids acted on corpuscles by laws of resistance. In that regard lubricity became a measure of hw slippery a fluid was.

Because of the clear boundary of geometrical forms, Newton's Anlysis was always based on uniform and smooth motions and deformations. He had no way of dealing with chaotic or rough systems, even with his Fluxions. Thus his analysis of fluids was doomed to result in less accurate results than his point mass analysis.

The definition of a fluid is crucial. Considering it to be a resistive medium eliminates many of the contradictory behaviours that then arise!

For me

Space is a fluid that consists in contiguous regions of varying density, which are fractally distributed dynamically.

The contiguity of spatial densities is crucial in this dynamic setting. There is for me no container space, just varying density space. Denser space pushes through less dense space, but also denser space can fragment by rotational action in less dense space., and this is directly related to the barycentres of a rotating element and the viscosity within that dense region.

The contiguity of space means that this rotation and change is always transmitted my strain propagations throughout space, but at the same time moving Fractl " masses" also displace the status at the time.

There are 2 gyres of note , the third being a fixed radial gyre. The first gyre expands, while the second contracts. The notion of clock or anticlockwise is relativistic, although if a gyre actually stops spinning and speeds up in the opposite direction that I would call non relatistic variation.

The behaviour of these gyres  in combinations would constitute a proper area of research in fluid dynamics.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #43 on: February 09, 2014, 02:25:15 AM »

The following principle suggests itself:
In any region of uniform density a uniform viscosity exists which transmits strain through that density in a time and material dependent manner. Furthermore, at the boundary of such a region of uniform density reflection and refraction and diffraction of strain occurs according to Snells Laws.

The deformation in the the region is a density deformation and is spherical in behaviour.

In addition a general principal of Newyonial fluid motive is that it is equivalent to energy and transforms into different firms of energy the chief among which is usually called Force or Pressure. This motive promotes rotational pressure (force) as its first transformation .

The barycentres of these rotational forms play a significant role in the geometry of the dynamic equilibria that result in terms of elasticity and viscosity.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #44 on: February 09, 2014, 08:47:58 AM »


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