  We re-visit the calculation of mode oscillations in the ocean of a rotating
neutron star, which may be excited during thermonuclear X-ray bursts. Our
present theoretical understanding of ocean modes relies heavily on the
traditional approximation, commonly employed in geophysics. The approximation
elegantly decouples the radial and angular sectors of the perturbation problem
by neglecting the vertical contribution from the Coriolis force. However, as
the implicit assumptions underlying it are not as well understood as they ought
to be, we examine the traditional approximation and discuss the associated mode
solutions. The results demonstrate that, while the approximation may be
appropriate in certain contexts, it may not be accurate for rapidly rotating
neutron stars. In addition, using the shallow-water approximation, we show
analytically how the solutions that resemble r-modes change their nature in
neutron-star oceans to behave like gravity waves. We also outline a simple
prescription for lifting Newtonian results in a shallow ocean to general
relativity, making the result more realistic.
