Traditional weather forecasting models are physics-based and rely on supercomputers. AI-based models base their predictions on past weather instead, giving them faster run-times--and some serious blind spots. (Image credit: B. McGowan; research credit: Y. Sun et al.; see also S. Nath and T. Palmer; via Gizmodo)
During my thesis, researching ways of flow around rocks and ships near the surface of water, I found a set of equations that can be used to model these weirder shapes. One example was the lemon curve, which you saw as the cricket ball simulation I showed earlier. The other is a generalised version of these that allows one to customise the location of bumps on the surface of the solid. The following plots were made in python.
Lemon curves (name courtesy of my fabulous sister @mrunmione) - the shape used to model a cricket ball
Crocodile curves (because they literally look like crocodiles)
Why are they important? ↓
It is important that when you model obstacles, you do so with at least second-differentiable functions, which means that they can be differentiated at least twice without behaving badly.
This is due to the nature of equations used to model fluids, called the Navier Stokes equations, which is based on Newton's 2nd law of motion, the force applied on an object is proportional to the acceleration (which is where the 2nd derivative comes into play).