Dr. Tetsuya Fujita, a.k.a. Ted, a.k.a. Mr Tornado was a meteorologist who spent most of his career at the University of Chicago. When I was in graduate school, I was down the hall from him and a friend (Eric) was one of his students. One day, Eric told me a Ted story.
Dr. Fujita held up a book on fluid dynamics (one of the central subjects for studying meteorology) and said to Eric "See this book? I only know chapter one." (maybe it was 'use'. Been a few years.) At the time, I thought it was more than a little exaggerated. And it probably did have a fair amount of exaggeration (Ted wasn't above such things). But, as I've continued my career and studies, I see more and more truth and wisdom in that comment.
I don't know about that particular book. But as I re-open math and science books I read years or decades ago, I'm continuing to find meaning and importance very early in the text. Not because I didn't learn enough of the early chapters to do well in class and tests, or to be able to apply the knowledge in later years at work. Rather, because as I've worked more on the subject, or learned more outside it, I see that there are more and more connections to 'chapter one' material. In that case, there's a lot of merit to looking back at chapter one and seeing how much deeper a knowledge I (you too, probably) can get from the later viewing.
13 April 2016
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3 comments:
Along those same lines, a first-order equation that really matters for hydrodynamics is the wave equation. If you consider that along the equator, the coriolis effects cancel out, then you are left with is a surprisingly simple formulation. Climate scientists make a mistake when they bypass the simple first-order physics to explain what they think are complex behaviors.
Sorry WHUT, thought I'd approved the post this morning.
Wave equations are second order mathematically. I guess you mean first order physics instead?
Climate folks don't ignore waves. One of the standard texts for geophysical fluid dynamics, a central field for climate dynamics, is Adrian E. Gill's _Atmosphere-Ocean Dynamics_, 1982, Academic Press. He explains or examines practically everything by way of waves, and is not unique in this.
For a specifically equatorial climate feature, consider the El Niño - Southern Oscillation. One of the standard educational starting points in examining it is to look at the ocean and consider it in terms of being driven by an eastward propagating Kelvin wave, and westward propagating Rossby wave. This also shows why you won't hear about this unless you're in an introductory geophysical fluid dynamics class. The real ENSO is fundamentally coupled between the ocean and atmosphere. These ocean waves are strongly modified by the atmosphere -- to the point that you can't make a good El Niño prediction looking only at the ocean. So when you see a modern discussion of ENSO, you'll see much more complex things than the waves.
The Kelvin and Rossby waves point to one of the lovely complexities of the climate system. As you note, the coriolis force is zero at the equator. But neither wave would exist if the earth didn't rotate. Kelvin waves require a wall. Normally it is a physical wall, like a coast line. But the line where coriolis goes to zero (the equator) also works. But coriolis also has to be nonzero elsewhere for the wave to exist. Rossby waves exist only on a rotating spheroid (the coriolis force has to change with latitude).
But, speaking of Rossby waves, they were also used for a time as a means of weather prediction. And some of the language from Rossby wave dynamics is still used. Unfortunately, reality again turns out to be too complex for this simple approach. iirc, the last time a new model based on this approach was implemented for forecast guidance, it was in the late 1950s, the 'equivalent barotropic' model.
How about the wave equation when it applies to QBO?
Most climate scientists apparently deduce the QBO cycles are a natural response, but I can verify that they are clearly the result of a forced response. In that case the details of the wave equation are irrelevant, as the forced response is essentially a scaling and frequency modulation of the forced input:
http://contextearth.com/2016/03/06/forced-versus-natural-response-not-a-secret/
This is a very critical "Chapter 1" analysis technique that may be missing from climate science course material.
With some more work, ENSO may be proven to also be a forced response system, much simpler than a coupled ocean-atmosphere natural response.
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