I'm writing a major paper on fluid flow in vortices (think tornado) and the solutions don't generally exist at all. Truly original research is not required, but I want to give a rigorous proof of the Navier-Stokes eq, starting from the basic continuity equation, explain their assumptions (continuous flow, no quantum behavior), and then go on to illustrate an analytically solvable case where we assume axisymmetric flow and inviscid flow. Both these conditions reduce the complexity considerably, but the few papers published i can find still use rather sophisticated dimensional analysis to solve the equations or even more powerful (and less intelligible to me, since i haven't seen them yet) Lie algebra symmetry groups. I need some suggestions on where to find more analysis of exact solutions for fluid flow in a vortex. Or how to modify my paper so I can actually make at least SOME calculations, on my own, in a day or two. This thing has to be written and in by wednesday or thursday at the latest. I appreciate any advice or discussion. Also, I really want to use lagrangian dynamics or hamiltonian dynamics to solve these problems but it seems that calculating the kinetic energy field is very difficult, and i'm not sure whether the potential energy field would be anything besides the gravity potential or whether it would simply be too difficult to calculate because of some other factors i am unaware of. Both would obviously be necessary to use either dynamic analysis.