Wait, Which Notation Do I Use?

Being a math/atmospheric science student with a background in engineering is really cool most of the time. But unsurprisingly, it has some less pleasant moments. In particular, conventions have been making my head spin.

I’ve known for a long time that physicists and mathematicians use a different notation for which of theta and phi is the inclination angle and which is the azimuthal angle in spherical coordinates. And now it gets better; geophysical fluid dynamics uses yet another convention with regards to spherical coordinate notation.

In a fluid dynamics class, the streamfunction is usually defined with the x-velocity u equal to the partial derivative of the streamfunction with respect to x, and then the y-velocity v is equal to the partial derivative of the streamfunction with respect to y. In geophysical fluid dynamics (or at least my book/class), those signs are reversed.

Fluid dynamicists refer to the material derivative and write it as Dy/Dt; dy/dt implies that y is a function only of t. Physicists call the material derivative the total derivative and write it as dy/dt.

Why do I know about all of these, and why do I care? Because I’m either in classes now or was in classes last semester using all of these conventions, and courses or disciplines using each of these conventions will be on my qualifying exams. It’s fun, by which I mean very, deeply confusing. The joys of being interdisciplinary.

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