Abstract
Globally balanced equations for a localized meso-scale disturbance embedded in a large-scale flow are derived. The “globally” means that integrated(i.e., averaged) quantities over the meso-scale region are subjected to the equations. The integrated quantities are the velocity potential and stream function of the horizontal velocity, and the energy. From these, large-scale counterparts, which are integrated (i.e., averaged) on the outside surface of the meso-scale region, have been subtracted.
The results show the followings. The translating velocity of the meso-scale disturbance is equal to the large-scale velocity averaged just outside of the disturbance, to O(Ro) (i.e., neglecting O(Ro2)), where Ro is the Rossby number of the large-scale flow. The averaged-subtracted energy is conserved, to O(Ro). Both the averaged-subtracted velocity potential and stream function oscillate with a frequency f (equal to Coriolis parameter), to O(Ro). In particular, if the averaged-subtracted velocity, potential and stream function are, respectively zero and equal to the averaged-subtracted energy divided by f initially, then they remain so to O(Ro).
