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May 31st, 2017, 09:00 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 346 Thanks: 26 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: 2,103 Thanks: 704 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: 346 Thanks: 26 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 hydrodynamics, modelled by fractal chaos, are selfsimilar 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  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,103 Thanks: 704 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
 
June 6th, 2017, 03:32 AM  #5 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,591 Thanks: 546 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.


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chaos, number, quadratic, reynolds, squared 
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