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According to the previous discussions in this thread:  http://www.fractalforums.com/let%27s-collaborate-on-something!/developing-fractal-algorithm-for-fluid-dynamics/ (http://www.fractalforums.com/let%27s-collaborate-on-something!/developing-fractal-algorithm-for-fluid-dynamics/)
and the consideration of an asymmetric potential field in fluid dynamics or in other words that the potential theory with conservative vector fields applied on gravity or magnetism is not applicable in fluid dynamics.
Reasons:

• 1.) A classical perspective of a potential field rejects the rules of mechanics that in a closed mechanical system all forces must equilibrate each other. Thus a gap in the force distribution is not possible. Instead the correlation between static pressure and speed has only an irreversible straight forward behavior. This is because the static pressure represents newtons 2nd law of motion the necessary force for getting a mass out of it's inert nature. Thus the represented static pressure is an equivalent of acceleration due a constricted fluid stream.
• 2.) Incompressible fluids (the most conservative nature of fluids) cannot store energy. But storing or exchanging energy with a repository is necessary for the potential idea to work. Such as in the compressible condition where we have volume work to act as a repository of energy. But unlike classical potential theory the volume work does not obey the rules of mass continuity but rather is oriented on it's own relation between pressure and volume expansion leading to a classical wave behavior. This leads to dualistic effects within fluids where we have compressible - wavelike fluid behavior interaction with a potential coupled with turbulence from incompressible behavior. Interactions with a potential field express themselves in volume work (air) causing noise waves or in terms of a gravity potential leading into waves in a river torrent
• 3.) Energy and Volume Equilibrium within Fluids is achieved by laminar separation bubbles, which finally turn into vortices.

Conclusion: Other analytical methods beside the potential theory are not known. Analyzing instationary and turbulent fluid behavior has yet been so far restricted on non-linear analysis which do not provide an analytical explanation of the processes happening inside turbulence. So there comes a famous quote form Werner Heisenberg: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."
(recent publications: http://elib.uni-stuttgart.de/opus/volltexte/2002/1072/pdf/dissertation-maucher.a4.pdf (http://elib.uni-stuttgart.de/opus/volltexte/2002/1072/pdf/dissertation-maucher.a4.pdf) )

Solution:

Why do fluids attach to receding surfaces? Arguing in borders of classical newton mechanics there is initially no answer why a piece of mass should follow an receding trajectory and what constraints it to it. Thus the discussion of explaining these phenomenons like dynamic lift on airfoils or the Coandǎ-Effect is currently made by quite awkward explanations they are not capable to give a clear answer. e.G.:

• Why does turbulence happen only in an divergent flow
• Why does the stream only attach to a certain degree and then detaches with a turbulent motion
• How can Fluid particles attach to receding surfaces
• Why does the inclination of the bending to a trajectory play a major role.

The explanation is this:
http://www.youtube.com/v/nAiPtgJsmOw?hl=de_DE&version=3

Attaching of Fluids on receding surfaces (aka laminar separation bubble) happens because of a given pressure. when a certain trajectory of surface is given to recede the streamlines of fluids a gap between the surface trajectory and the fluid streamline occurs. Thus there is automatically a gradient from the pressurized fluid towards a resulting vacuum at the wall. The pressurized fluid mobilizes acceleration from it's pressure to fill the gap. But this can only happen against the inert nature of the fluid. As visible in the simulation a certain reaction inertia is given unable to follow any given trajectory but only such where there is enough acceleration energy available. Sharp edges thus causes locally a strongly increased acceleration gradient in the flow field. The pressure given from the fluid cannot follow any gradient resulting in small gaps or bubbles they hold a vacuum in the prototype stage or are filled with trapped Vortices in more macroscopic scales.

Opportunities:

This idea of explaining laminar separation bubbles opens up new opportunities and tools to analyze and understand instationary fluid motion with the opportunity to develop analytical rules they can describe instationary motion in fluids.
Applied in an algorithm through perturbation or iteration we can describe fluid motion extremely precise with actually a minimum of render-power compared to what is today necessary to simulate fluid motion. And it will be far more precise.
With this method we can develop algorithms that restricts it's render power only tho the parts in the solution which have a non divergent solution. All other calculations within the volumes are void because they are converging, stable and not influencing the final result.
Yet all the numerical approaches are not entirely proven to be entirely correct. E.g. Navier-Stokes, the fundament of most simulation methods like Direct Numerical Simulation are yet only proven in 2 dimensions. it will also eliminate or overcome it's numerical feedback that is caused the more we increase the precision. because this approach to the solution is not influencing itself like all non-linear methods.

These New approaches looking at fluid motion opens up an abundance of describing many unknown phenomenons on similar rule set - like quantum motion, which has indeed many parallels to fluid dynamics. We e.g. could describe quantum particles as vortices. within a medium of zero viscosity very odd things happen to the fluid solution which come very close to the mystic behavior of quantum mechanics.

Thanks freshNfunky . At last got round to reading your post and analysis .

Did you get to look at the Work by Claes Johnson? His numerical resolution of the Potential flow problem, and the reworking of how aerofoils fly is very interesting and in my opinion important.

Your move towards bubbles is very interesting and well argued. I only have a general idea of how that is the way to go and that is because I promote the notion of Trochoidal motion as the fundamental natural one. I have used the term Grassmann Twistor or Grassmann Euler expression to denote such reference frames or arc segments, but essentially they are Fourier type extensive magnitudes, geometrically. I prefer Spaciometrically.



However I am deep in the process of translating the Grassmanns work and ideas, and so I am holding my breath on further analysis until I grasp these, as already they change everything for me! Especially the wrongheaded idea that mathematics can penetrate where good honest empirical data and research and observation cannot!

It is truly an Astrologers goal to seek immutable or knowable patterns in the data, but these come from the Data of empirical measurements and observations, not the other way round!

Why relativity ? That's easy. We each are individually important and our collective view requires it, or the collective view is false for some observer!

Why turbulence ? That again is easy. Infinite possibility requires it or we do not have infinite possibility at any scale! Thus fractal patterns are precisely what we are calling turbulence.

Of course we can never know all possible fractal patterns, and so we can never model all possible turbulence, but the nature of fractals means we can apply the simplest models and approximate to better results !

So let's do it with triangles first !