Briefly. The expansions used to describe the motions of fluids in a flow require repeated derivatives and that in itself is iterative. Then on top of that these equations do not admit to simplistic so called elegant solutions and have to be solved by iterative computational means after some simplification condition or assumption. So in my definition of fractal as the product of any iterative process/ procedure, the results from these efforts are fractal. By inspection by eye the results look fractal and develop fractal structures as each iteration is applied. It is assumed that the iterations represent the steps in time, but that is a whole other topic.

With regard to scale and self similarity work is being done to uphold the scale relationships between similar results in larger and larger systems.

My advice to any one thinking about the mathematics is to get ahead of the curve and realise that mathematical descriptions are all fractal, that is the result of iterations. If you can approach it that way then you will see something that older mathematicians have forgotten or pushed to one side.

I would start by researching the navier stokes equations and refreshing your vector math and  calculus all of which are iterative in nature.

thanks, in other words, the equations of motion and turbulence is resolved through numeric aproxs and iterating, fractals, turbulence and motion laws. : : :

regards

Not to my knowledge--the domains are completely different.  At the quantum scale, there aren't even atoms, let alone molecules or fluids.