Could anyone help me work through the following set of equations:
I found these online at
and I'm trying to work through them. I get the basics from this i.e. that if a water particle moves vertically it will be subjected to a buoyancy force due to it being surrounded by water of different density. However, I don't understand how the solution has worked i.e. how they went from one stage to the next. Could anyone provide more information about how this solution works?
My main aim here is to figure out how the Brunt vaisala buoyancy frequency is derived.