We applied the NSe to understand various forms of waves, among them the surface gravity wave, the internal gravity wave and the Rossby wave (both without boundaries), and the Kelvin wave.

(1) Which of these is your favourite wave, and what is it that you like about it (i.e., what distinguishes it from the others)? [10]

(2) Derive its dispersion relation, starting from the NSe and the continuity equation. State clearly the steps you take to simplify these equations, and how you apply the boundary conditions (if any). [15]