How do physicists model chaotic fluid motion like steam rising from coffee?

[Aria96]

Okay, this is going to sound a bit silly, but I was just watching the steam rise from my coffee mug this morning. I got stuck thinking about how the swirls move and mix with the cooler air in the room. It made me wonder how physicists even begin to model something so chaotic and ever-changing. Is the math for describing that kind of fluid motion fundamentally different from something more stable, or is it all under the same umbrella? I’ve never been able to wrap my head around where the line is.