29 January 2014
Science Tweeters to follow?
Yesterday I mentioned a few science tweeters. Today I'll ask you for your favorites on science. Any science.
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Thoughts and notes on science from another blogging Grumbine.
Welcome
I'll be trying what seems to be an unusual approach in blogs -- writing to be inclusive of students in middle school and jr. high*, as well as teachers and parents (whether for their own information or to help their children). To that end, comments will have to pass a stricter standard than I'd apply for an all-comers site. It shouldn't be onerous, just keep to the topic and use clean language.
I expect it to be fun for all, however, as you really can get quite far in understanding the world, even climate, by understanding this sort of fundamental. If I get too much less fundamental, let me know where I went astray.
* Ok, I concede that not many middle school students will get everything. Even a fair number of adults will find some parts hard to follow. Still, some middle school kids will have fun. And almost everyone will follow a number of posts just fine.
Please see the comment policy for details. And the link policy for details about that. The latter is more open than you might expect.
I expect it to be fun for all, however, as you really can get quite far in understanding the world, even climate, by understanding this sort of fundamental. If I get too much less fundamental, let me know where I went astray.
* Ok, I concede that not many middle school students will get everything. Even a fair number of adults will find some parts hard to follow. Still, some middle school kids will have fun. And almost everyone will follow a number of posts just fine.
Please see the comment policy for details. And the link policy for details about that. The latter is more open than you might expect.
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About Me
- Robert Grumbine
- In my day job I work on the oceanography, meteorology, climatology, glaciology end of my science interests, but I'm interested in everything, science or not. So I've also been on stage in a production of Comedy of Errors, run an ultramarathon, and been to Epidaurus, Greece, to see a production of Euripides' Iphigenia among the Taurians Prior to starting the current job, I was a post-doc in oceanography in the UCAR ocean modelling program, and earned my doctorate from the Department of the Geophysical Sciences at the University of Chicago (1989). My undergraduate degree involved Applied Math, Engineering, Astrophysics, and Glaciology. Of course I don't speak for my employer, whoever that may be.
2 comments:
Dr. Grumbine: What is your opinion on the shortcomings of the Boussinesq approximation, if any, in oceanic models ? ( i refer to ignoring dro/rho tems unless multiplied by g)
but it gets the volume wrong...this has been causing me unquiet and anxiety for some tie, have you any thoughts ?
sidd
Sorry about the delay sidd. Back when I was taking geophysical fluid dynamics, I was concerned about the approximations we would make, including the Boussinesq. As I remember it, of all the approximations, Boussinesq was one of the best -- as long as the ocean is markedly less than 200 km deep (the average being a bit less than 4 km, and extreme is about 10 km). Rather, the scale of vertical motions in the ocean. Since I was concerned with deep convection in the ocean, the depth of the ocean was what I had to pay attention to.
Volume is a different concern. The Boussinesq approximation applies only to the conservation of momentum equation. Mass conservation is in the drho/dt + div(u*rho) = 0, which is accurately simplified to div(u*rho) = 0 if you ignore sound waves in the ocean. But mass is a somewhat different issue than volume. Volume (and density) conservation properly requires tracking conservation of energy (temperature) and salinity. But, again, both of these are indeed tracked in ocean models, necessarily.
The potentially ugly part comes in dealing with the effects of salinity changes on density, through to volume (sea surface elevation). It is common to treat the mass conservation from surface waves as d(surface)/dt + div(u*H) = 0. This ignores density variation, which is a good, but not perfect approximation. Separately precipitation/evaporation and freeze/melt of ice are tracked in the salt conservation, but may not be allowed to affect the sea surface height, which is a less good approximation.
This is where I'd look in a model for concerns about volume (and thence sea level). Some do indeed include the sea level effect of the temperature and salinity variations.
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