How do you apply classical mechanics to turbulence?

how do you apply classical mechanics to turbulence?

chaos theory

elaborate.

tl;dr: there is no way to precisely describe turbulences with formulas and shit

that's also why the weather forecast sucks donkey balls

Nonlinear dynamics. Prerequisite class is differential equations.

Basically you can describe the features of a turbulent flow and estimate the radius of the little vortexes. Just because it is chaotic, doesn't mean you can't predict the emergent bits.

can you predict the positions of the vortices?

To answer your question OP, it has been very difficult to make precise analysis of turbulence to the same degree that we can analyze mechanics. You can get some pretty decent estimates, but unfortunately the amount of variables in any turbulent system can get pretty nasty. This is also how computer scientists model randomness (the other method is by using the linear congruential method) because while they are predictable in theory, there is simply an impossibility in knowing the state of every factor in the system. In short, you could apply classical mechanics, but it would be impossible to analyze in any reasonable amount of time assuming you could gather all the necessary data in the first place.

kinda, not really. So vortecies don't like each other so you do your equations to get the radius and then you pack them into the geometry and it gets you an upper bound. There's more to it, the class kicked my butt.

All pressure conduit, force main, closed-circuit analysis relies on approximations. They're pretty accurate though. The only important thing is to have the desired flow, velocity, pressure, etc anyway. Who cares about the vortexes.

Hell no.

But user, we use classical mechanics to model turbulence. Turbulence ain't a quantum phenomenon.

No, we have fomula to model turbulence, see the Navier-Stokes equations.

The issue is the equations just explode and require huge amounts of computational effort.