On the Relation between Vorticity, Deformation and Divergence and the Configuration of the Pressure Field

Theorems for the vorticity, deformation and divergence are developed for quasi-horizontal frictionless motion. The divergence theorem is used to investigate the validity of the geostrophic approximation, and it is found that the balance between the Laplacian of the pressure field and the vorticity is appreciably influenced by the deformation, while the divergence is relatively unimportant. The vorticity theorem and the deformation theorem are combined to obtain a prediction quantity which is related to the absolute vorticity and permits treatment of the fields which are more general than the geostrophic field. Some charts are produced to show the magnitudes of the various quantities in a mature storm.