Vector Calculus Weather

As it happens I did a lecture today about vector fields as part of my module on vector calculus. Whenever I did similar lectures in the past I used the day’s weather map as an illustration, so this morning I downloaded what turned out to be a particularly dramatic example. The curl of the velocity field around the weather system off the west coast of Ireland this morning was definitely non-zero…

Storm Callum turned out to be not as damaging as feared. Apparently it was rather windy in Maynooth overnight, but I slept right through it.

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A (Physics) Problem from the Past

I’ve been preparing material for my new 2nd year lecture course module The Physics of Fields and Flows, which starts next week. The idea of this is to put together some material on electromagnetism and fluid mechanics in a way that illustrates the connections between them as well as developing proficiency in the mathematics that underpins them, namely vector calculus. Anyway, in the course of putting together the notes and exercises it occurred to me to have a look at the stuff I was given when I was in the 2nd year at university, way back in 1983-4. When I opened the file I found this problem which caused me a great deal of trouble when I tried to do it all those years ago. It’s from an old Cambridge Part IB Advanced Physics paper. See what you can make of it..

(You can click on the image to make it larger…)

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