Not really, maybe it is a bit random like Brownian Motion.

I had thougt of automobile traffic on roads to be similar to 1D compressible flows, where traffic jams are like shock waves. As a graduate student I thought the idea was novel, but turns out others had thought about it. 🤣

A stratified fluid has some layers stacked vertically due to changing temperature (as is the case in atmosphere) and changing density or both (as is the case in ocean). Typically the temperature or density decreases as we go up, in which case we say the fluid is "stably stratified". However since these system experience a lot of external energy input (think radiation, waves or circulation), the fluid is pushed around and is essentially in a turbulent state. This idealized system can be studied theoretically / computationally (in a periodic box) and experimentally (in a salty water tank) as an analogue for the atmosphere and ocean.

You're welcome 😀

Navier Stokes is the most common model for most phenomena when the fluid can be assumed to be a continuum. But when

• it involves particles / multiphase flows / phase change / chemical reactions, extra equations are needed
• in microsccopic regime (small devices like a DNA sequencing machine) / rarefied regime (hypersonic fluids) the fluid molecules are too far apart, so it is no longer a continuum. Other models like Molecular dynamics or Monte Carlo methods or Lattice Boltzmann methods work best here.
• in highly turbulent flows, you can't simulate the full Navier Stokes due to limitations in computational resources. Then some turbulence modelling is needed to mimic diffusion at small scales.

In games what I think they do is a technique called smooth partical hydrodynamics, which simply put does not solve the Navier Stokes equations (the preferred classical model for fluids), but moves solid spheres around which collide and interact.

The right way would be to solve the full 3D NS equations, but like you said it is very expensive to do. But doing a 2D simulation on a laptop is very much possible. This hands on series is a good start

https://lorenabarba.com/blog/cfd-python-12-steps-to-navier-stokes/

There are also other models like a lattice boltzmann equations which this web app solves

https://physics.weber.edu/schroeder/fluids/

For more detailed study a theoretical book would be Fluid Mechanics by Kundu and Cohen and a computational book would be CFD 3 volume series by Hoffmann and Chiang.

There are two kinds of geophysical flow studies one can do. 2D simulations where you use models like shallow water equations. Then you deal with

• Velocity
• Reynolds number (which implies some viscosity)
• Froude number (or gravity)
• Rossby number (or Coriolis force from Earth's rotation)
• Total energy (so you know when it is in a statistically steady state)
• Density only if you add many layer
• Boundary conditions (only if it matters, can be avoided)

You can also do a 3D simulation, but often we use the Boussinesq equations, in which density is approximated as a passive scalar.

This is only the setup, but there is a rich set of phenomena one can aim to simulate with.