Sure, and a boiling pot of water has chaos in it, you can't predict fluid dynamics well enough to predict the path of any one molecule.
But you can most definitely predict that the water will boil and then boil off.
First of all while I know nothing about fluid dynamics, I know it has no ability to predict anything about individual water molecules, not because fluid dynamics is some fake science but because the scope of fluid dynamics is not individual water molecules. If you want to know the position of individual molecules of water you do not use fluid dynamics.
All real systems are chaotic systems, and all systems can be modeled based on individual interactions of molecules if we are talking about real matter, at least in principle. I say at least in principle because the best simulation that we can do is maybe 1000 molecules of cesium, and that would take a supercomputer to do it. We have not yet simulated enough molecules to fill the head of the pin yet, there must be a billion molecules of shit that can fit on the head of a pin.
Now if you want to track individual molecules of water then you need to simulate individual water molecules, that is a chaotic system, it is chaotic because it should be apparent to you that the initial position of the water molecules influences the final position of the water molecule.
Now thankfully some really smart people came up with fluid dynamics, which I do not know anything about, but I would hazard to guess that it is a closed form solution, any solution worth it's salt is a closed form solution. If you need to know stuff like the flow rate or the pressure of the water, then there is some nice simple equation that you can use to find it. Now if you need to know the position of each molecule then you need to do a full simulation of each and every water molecule.
If fluid dynamics was not available then you have no recourse but to do a full simulation (simulate all individual water molecules) to find out stuff like flow rate and pressure. Because fluid dynamics has closed form equations, we can just plug numbers into a simple equation and not need to simulate all the water molecules.
Now I am unaware of any closed form solution for climate, believe me if it was easy to find closed form solutions then it would have been done a long time ago. Without a closed form solution we have to simulate climate down to all the individual interactions of each particle in a climate system or atleast maybe in chunks of say a billion atoms, of course we can not do that with current computer technology. This is why I have said in the past that we need quantum computers to simulate climate to a necessary degree to draw conclusions, I am not saying we need quantum computers just because it is a cool thing to say.
Now I am not sure if closed form solution is the proper term, I know of systems which are very well described by equations but to solve it is an iterative process and not what I considered closed form, an AC power system simulation is an example of an iterative solution. I guess by closed form, I mean an equation that can be written down on a single piece of paper, or somewhere in that vicinity.
E=MC^2 that is a closed form solution, you in principle do not need to use that equation, you can find the energy of any mass by simulating the fission/fusion process individual atoms and if your simulation is rigorous then the answer you get is the exact same answer as if you use E=MC^2 in the first place. Now solving E=MC^2 takes maybe 10 seconds to find E, doing it by simulating individual molecules of matter would take all the computer power in the world and then some for maybe at best a million molecules of something.
