My Math Forum Reynolds number squared -- quadratic chaos?

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 May 31st, 2017, 09:00 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 404 Thanks: 27 Math Focus: Number theory Reynolds number squared -- quadratic chaos? If the Reynolds number quantifies the transition from laminar to turbulent flow, might its square represent smaller, chaotic structures; i.e., of a quadratic map?
 June 5th, 2017, 01:13 AM #2 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,155 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions For what reason? Remember that the Reynolds number is $\displaystyle Re = \frac{vL}{\nu}$ where v is the velocity of the fluid (m/s), L is the characteristic length of the system (m) and $\displaystyle \nu$ is the kinematic viscosity of the fluid (m$\displaystyle ^2$/s). Why would squaring it change it's meaning to something else?
 June 5th, 2017, 08:15 PM #3 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 404 Thanks: 27 Math Focus: Number theory I speculate that, just as laminar and turbulent flows find resonances in their "transition", so Reynolds numbers below laminar, and above turbulence, have resonances which relate to fluid, statistical or thermal behavior. QED's Feynman graphs are dimensionless and Reynolds numbers are too. Both their gradients can indicate a power series. For both graphs and experiment, they eventually approach the infinitesimal, even interacting unto the quark scale and back. Aero- or hydro-dynamics, modelled by fractal chaos, are self-similar even beyond physics. Consider the complex Mandelbrot geometric mapping, that of a simple quadratic equation. It could rely also on any real number, but there are simpler, discrete systems, often found in physics. I considered laminar flow and its lower limit -- likewise the link between turbulent flow and its upper limit. In those regions we might find geometric novelties. Most may have not been found yet because higher order experiment and theory rely on second, third, fourth...powers, even though such issues have been considered elsewhere. With a second power we have a uniqueness factor of at least 2,000 more, for a third 4,000,000 more, etc.
June 6th, 2017, 01:36 AM   #4
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Quote:
 Originally Posted by Loren I speculate that, just as laminar and turbulent flows find resonances in their "transition", so Reynolds numbers below laminar, and above turbulence, have resonances which relate to fluid, statistical or thermal behavior. QED's Feynman graphs are dimensionless and Reynolds numbers are too. Both their gradients can indicate a power series. For both graphs and experiment, they eventually approach the infinitesimal, even interacting unto the quark scale and back. Aero- or hydro-dynamics, modelled by fractal chaos, are self-similar even beyond physics. Consider the complex Mandelbrot geometric mapping, that of a simple quadratic equation. It could rely also on any real number, but there are simpler, discrete systems, often found in physics. I considered laminar flow and its lower limit -- likewise the link between turbulent flow and its upper limit. In those regions we might find geometric novelties. Most may have not been found yet because higher order experiment and theory rely on second, third, fourth...powers, even though such issues have been considered elsewhere. With a second power we have a uniqueness factor of at least 2,000 more, for a third 4,000,000 more, etc.
I have no idea what you're talking about. Are you getting information from one of those fictional journal things again?

 June 6th, 2017, 03:32 AM #5 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,798 Thanks: 634 Math Focus: Yet to find out. There seems to be a flood of posts that are just words mashed in together without aim or purpose. Totally incoherent sentences all jumbled together.

 Tags chaos, number, quadratic, reynolds, squared

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