Hi all! I defended my Ph.D. thesis back in 2019 and I also served as the creator and moderator for the subreddit r/FluidMechanics for a long time. I think with that I have gathered enough experience and courage to answer some of your queries. Some broad topics that I can answer questions on are:
- computation fluid mechanics
- scientific programming and HPC
- nonlinear shallow water equations
- statistical description of turbulence: spectra, energy budget etc.
- experimental methods: PIV
- stratified turbulence
- academia
- navigating your career pre- and post-Ph.D.
Ask away!
For geophysical CFD, what are typical values you deal with?
- Viscosity
- Density
- Velocity
- Reynolds number
- Simulation timestep
- Total simulation elapsed time
- Total number of simultaneous unknowns solved for
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.
So are you treating the Earth’s crust as a shallow fluid layer? Or the mantle underneath? I would think the mantle is too thick for shallow water equations.
Usually for the troposphere or even the atmosphere and the ocean this can be a good model. As you said, I doubt if it can be used to represent lava flows under the earth - something a geologist would know and I am not one. 😀
I have been wanting to learn about computational fluid mechanics because I think fluid flow simulations look cool and would be a great programming project. But at the same time, water never really behaves like water in video games. I imagine because it is a hard problem to solve. What resources (textbooks, videos, etc.) would you recommend for someone who is interested in learning about fluid mechanics but has only dealt with fluids in an introductory engineering course many years ago?
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.
Thanks! The Jupyer notebooks seem like a good starting point. I had used Burger’s equation but it was from the point of view of using it as a nonlinear dynamical system for state estimation, rather than from a fluid mechanics understanding of it. Are the textbooks you mentioned the recommended standards for this field?
Do you ever stare at a crowd of moving people through a busy street, and think “I could model this”?
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. 🤣
