A note on a geophysical fluid dynamics variational principle

Abstract

A variational principle for an inviscid stratified fluid on a beta plane is developed for horizontal flows. For the special case of solenoidal flow on an f plane, it is shown that a certain velocity gradient invariant can be used to develop simple solutions to the equations of motion. The solution forms are critically dependent on relative magnitudes of the squared local vorticity and the squared total deformation.