Matsuno (1966) discovered equatorial Kelvin waves, which propagate eastward and have no meridional velocity component. It is also possible to have oceanic "coastal" Kelvin waves, such that the currents are everywhere parallel to the coastline. A coastal Kelvin wave propagates parallel to the coast.
Consider a coastal Kelvin wave in the Northern Hemisphere. The wave is propagating along a north-south-oriented "west coast" with water to the west and a continent to the east. Does the wave propagate north or south? Include a sketch that shows the spatial structures of the height and current fields.