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Surpising that these physical models can outperform computers! I would have thought surface tension and gravity would mess up the scaling in the physical model.

by fovc 10y ago

Surpising that these physical models can outperform computers! I would have thought surface tension and gravity would mess up the scaling in the physical model. Is the problem in computer simulations that we don't have the equations, or that we don't have the computing power?

mathattack 10y ago
Both. In terms of computing power, think of the Butterfly effect: small changes in initial conditions produce enormous differences in outcomes. Also, the models aren't constrained by what we think the equations should be. In a sense, the equations are just a model of a more abstract kind rather than physical. Of course for the reasons that you listed physical models aren't perfect either.
cossatot 10y ago
Scaling is a very hard problem[0], but it's easier in these sorts of fluid systems where the materials have a simple Newtonian viscosity and the temperatures and other parameters don't change dramatically throughout the model. Contrast this with solid Earth or (I think?) atmospheric modeling, where those changes must be represented correctly by different materials. Nonetheless, for lots of problems in earth science, new computational models are still benchmarked to analog models. The other problem with analog modeling is that can be pretty hard to measure the full 3D velocity field, stresses and strains, and that sort of thing, which are explicit in computational models. Computer-aided particle tracking has made this far better for analog modelers in the past decade or two, though. [0]: A great reference for this is M King Hubbert's 1945 paper in which he considers whether it's possible to pick up the great state of Texas with a crane: https://www.depts.ttu.edu/gesc/Fac_pages/Yoshinobu/4361_5361_Folder/2013-readings/Hubbert,%201945%20Strength%20of%20Earth.pdf https://www.depts.ttu.edu/gesc/Fac_pages/Yoshinobu/4361_5361... (Hubbert is most famous among non-geologists for peak oil theory, and most famous for geologists in considering the role of pore fluid pressure during faulting).
b_emery 10y ago
We have the equations, its the computing power that is the limiting factor. You can do a full DNS (direct numerical simulation) of fluids on the order of a few cubic meters. That will simulate flow to the particle, and fully turbulent, with Reynolds numbers (Re) on the order of 10^6 (IIRC). Re goes up proportional to length scale, so if you want to do a km or so, multiply this by 10^2. This is way ocean models parameterize turbulence (large eddy simulations (LES), and Reynolds Averaged Numerical Simulation (RANS) for example). It's also why observational oceanography is still done.
- smhost 10y ago
  Thinking about what your wrote is aesthetic to me for some reason.
- pdm55 10y ago
  I was recently at an applied maths seminar. The speaker had been working on the main "over the horizon" radar in Australia for over 40 years. It was amazing to me that he could map ocean currents with radar!
sliverstorm 10y ago
scientists have still not invented equations that can fully capture the nuances of water moving through a river. -- America’s Last Top Model (http://99percentinvisible.org/episode/americas-last-top-model/ http://99percentinvisible.org/episode/americas-last-top-mode...)
- b_emery 10y ago
  We have have the equations [1], we don't have the computer power for a river. Observe the nuances of water moving around a square: https://www.youtube.com/watch?v=c8zKWaxohng https://www.youtube.com/watch?v=c8zKWaxohng [1] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equation...

by fovc 10y ago

mathattack 10y ago

Both. In terms of computing power, think of the Butterfly effect: small changes in initial conditions produce enormous differences in outcomes. Also, the models aren't constrained by what we think the equations should be. In a sense, the equations are just a model of a more abstract kind rather than physical. Of course for the reasons that you listed physical models aren't perfect either.

cossatot 10y ago

Scaling is a very hard problem[0], but it's easier in these sorts of fluid systems where the materials have a simple Newtonian viscosity and the temperatures and other parameters don't change dramatically throughout the model. Contrast this with solid Earth or (I think?) atmospheric modeling, where those changes must be represented correctly by different materials. Nonetheless, for lots of problems in earth science, new computational models are still benchmarked to analog models. The other problem with analog modeling is that can be pretty hard to measure the full 3D velocity field, stresses and strains, and that sort of thing, which are explicit in computational models. Computer-aided particle tracking has made this far better for analog modelers in the past decade or two, though. [0]: A great reference for this is M King Hubbert's 1945 paper in which he considers whether it's possible to pick up the great state of Texas with a crane: https://www.depts.ttu.edu/gesc/Fac_pages/Yoshinobu/4361_5361_Folder/2013-readings/Hubbert,%201945%20Strength%20of%20Earth.pdf https://www.depts.ttu.edu/gesc/Fac_pages/Yoshinobu/4361_5361... (Hubbert is most famous among non-geologists for peak oil theory, and most famous for geologists in considering the role of pore fluid pressure during faulting).

b_emery 10y ago

We have the equations, its the computing power that is the limiting factor. You can do a full DNS (direct numerical simulation) of fluids on the order of a few cubic meters. That will simulate flow to the particle, and fully turbulent, with Reynolds numbers (Re) on the order of 10^6 (IIRC). Re goes up proportional to length scale, so if you want to do a km or so, multiply this by 10^2. This is way ocean models parameterize turbulence (large eddy simulations (LES), and Reynolds Averaged Numerical Simulation (RANS) for example). It's also why observational oceanography is still done.

smhost 10y ago
Thinking about what your wrote is aesthetic to me for some reason.
pdm55 10y ago
I was recently at an applied maths seminar. The speaker had been working on the main "over the horizon" radar in Australia for over 40 years. It was amazing to me that he could map ocean currents with radar!

sliverstorm 10y ago

scientists have still not invented equations that can fully capture the nuances of water moving through a river. -- America’s Last Top Model (http://99percentinvisible.org/episode/americas-last-top-model/ http://99percentinvisible.org/episode/americas-last-top-mode...)

b_emery 10y ago
We have have the equations [1], we don't have the computer power for a river. Observe the nuances of water moving around a square: https://www.youtube.com/watch?v=c8zKWaxohng https://www.youtube.com/watch?v=c8zKWaxohng [1] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equation...