The basis of turbulence occurs from atomic compression. Each atom has energy associated with the movement of electrons. Atoms compose the liquid flowing through a particular vessel. At the turbulence tipping point, based on the speed of flow (additional momentum energy) and the size of the vessel relative to the mass of the liquid, the atoms and their individual atomic energy within the liquids mass become compressed. This is combined with the momentum energy associated with the liquid movement, to the point that creates friction, with friction leading to turbulence.
Given the environment of atomic mass, atomic homogeneity, atomic energy, and momentum energy are unique, the turbulence has the appearance of an unpredictable, chaotic environment. However, it is theorized the environment can be simulated with a large number of sample path outcomes leading to an understanding of the turbulence tipping point.. That is, the point at which flow transforms from smooth to turbulent.
Maybe Laplace was correct?!
In 1814, Laplace published what is usually known as the first articulation of causal or scientific determinism:
“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.”
— Pierre Simon Laplace, A Philosophical Essay on Probabilities
The Couette - Taylor Flow shows how turbulence is created as a function of liquid space and speed (velocity).
The Reynolds number - I guess my theory is not so original. What I call “atomic compression” is likely captured as viscosity by Reynolds.
“‘It seemed, however, to be certain if the eddies were owing to one particular cause, that integration [of Stokes equations of fluid motion] would show the birth of eddies to depend on some definite value of cρU/μ,’ explained Reynolds, introducing the parameter that bears his name. As the product of length (of an object moving through a fluid or the distance over which a moving fluid is in contact with an object or a wall), density (of the fluid), and velocity (of the fluid or the object) divided by viscosity (of the fluid), the Reynolds number signifies the relative influence of these effects. All instances of fluid motion—water flowing through a pipe, a fish swimming through the sea, a missile flying through the air, or air flowing around the earth—can be compared on the basis of their Reynolds numbers to predict the general behavior of the flow. A low Reynolds number indicates the predominance of viscosity (owing to molecular forces between individual fluid particles) in defining the character of the flow; a high Reynolds number indicates that inertial forces (due to the mass and velocity of individual particles) prevail.” - George Dyson from Darwin Among The Machines
It would seem a completely parameterized equation would not capture the turbulent tipping points. That is, the point at which flow transforms to turbulence. The Reynolds number would capture the relative likelihood of turbulent behavior in a static environment.