# Poincare wave

From AMS Glossary

## Poincare wave

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 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;*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.