Chaos, Turbulence and the Navier-Stokes equations

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As a member from an advanced species, one may wonder: how it is possible that we managed to go to the moon when, at the same time, we cannot accurately predict something seemly trivial as the weather? We can barely predict the weather conditions within 7 days or so. Why is that?

Well, the answer to this apparent inconsistency in our technology and knowledge lies in the theory of chaos, which is closely related to the theory of turbulent flows.

There is a philosophical debate about whether we live in a random universe or in a deterministic universe. However, what does that even mean?

To put it simple: in a random universe, there would be no consistent laws or equations that govern what happens there, only apparent laws that we, as intelligent beings, could infer to approximate and establish some sense to it. We would only be able to consistently describe it using statistics.

As the opposite, a deterministic universe would have consistent laws and equations governing it. Following this, knowing the initial state of a physical system and its governing set of equations, it would be possible to predict its future at any given time.

In the middle of these two distinct views of the universe, there lies the theory of chaos. It happens that, in a system that has many variables and is highly unstable and sensible to perturbations, even if we do know the initial state and its governing laws, we would only be able to predict the near future state of this system. Furthermore, as this system evolves from its initial state, it would appear that there are no deterministic laws whatsoever governing it, appearing to be increasingly chaotic and random. That is what chaos theory is about and there, in the middle of a random and deterministic nature, is where we find turbulent flows, or simply turbulence.

Видео Chaos, Turbulence and the Navier-Stokes equations канала Engineer Leo