From AMS Glossary
A gravity wave that is slow enough (low frequency) to feel the effects of the earth's rotation, so that the Coriolis parameter appears in the dispersion relation.
Within a channel in a rotating system, a Poincare wave has sinusoidally varying cross-channel velocity with an integral or half integral number of cross-channel waves spanning the channel. In the shallow water approximation the waves have dispersion relationship with squared frequency
in which f is the Coriolis parameter, k is the wavenumber along the channel, L is the width of the channel, n is any positive integer, and c is the phase speed for shallow water gravity waves;
in which g is the acceleration due to gravity and H is the mean depth of the fluid. Related to Poincare waves are Kelvin waves, which take the role of the mode with n = 0.