Quasi-geostrophic vertical mode (QG vertical mode)

A quasi-geostrophic vertical mode separates horizontal and vertical dependence of the streamfunction. With rigid horizontal boundaries and constant stratification, the vertical eigenfunctions are $\cos (n\pi z/H)$.

A barotropic mode has horizontal velocity independent of depth. It is the zeroth quasi-geostrophic vertical mode and usually has the largest gravity-wave speed and Rossby deformation radius.

A baroclinic mode has nontrivial vertical shear and at least one change of vertical structure through the fluid depth. Higher quasi-geostrophic vertical modes have smaller gravity-wave speeds and Rossby deformation radii.