It's been plaguing physicists for centuries

Fluids, as you learned in school, flow. And flow-physics is beyond satisfactory characterization for most real-life cases. Efforts to characterize phenomena like flow are usually based on differential equations that express the conservation of something or the other – mass, momentum, energy, etc. It’s easiest in this context to think of conservation of energy.

Energy is transferred and transported within the fluid in many ways, and turbulence includes all these ways in one word. This is not just word-play: depending on what constitutes “satisfactory” characterization, it can actually allow us to investigate the fluid’s behavior to within engineering accuracy.

We usually use models of turbulence: that is, we use an approximation that works well for some ranges of conditions, is accurate enough for the engineers, takes affordable computing time, and doesn’t take too long. (All those italicized words are subjective and represent potential complications.)

A more rigorous alternative is to resolve turbulence: more accurate, but often too expensive. At least at present.

If you’re looking for more detail, this is a good place to start. Read it through, note the terms and concepts that you didn’t follow, and then switch to a recognized text-book. Resist internet-searches at all costs.

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