Motion on a β ‐planet

It is well known that the standard β ‐plane is not a physical object. As a consequence, angular momentum is not conserved by the related flow equations. The flow equations for a β ‐planet with linearly varying Coriolis parameter and for an infinitely extended β ‐tube are derived in order to see whether these shortcomings can be removed while retaining the simplicity of the β ‐plane equations. The equations conserve axial angular momentum, but the β ‐planet offers no simplification with respect to the spherical case. However, the hydrostatic β ‐tube equations are isomorphic to those of the β ‐plane. Thus the standard β ‐plane equations also deal with flows on a physical surface. Copyright © 2010 Royal Meteorological Society