Abstract
The Q-vector in a quasigeostrophic system (Hoskins et al. 1978), which represents the tendency of geostrophic flows to destroy their own geostrophic balance, is a useful tool in diagnosing ageostrophic circulations. Recently, a 3-dimensional extension of the Q-vector was obtained in a quasigeostrophic system, and it was termed the C-vector (Xu 1992). On the other hand, the Q-vector was generalized into a primitive system (Davies-Jones 1991) and an ageostrophic circulation equation which is similar to the Q-vector equation in a quasigeostrophic system was obtained.
In this note, in an f-plane, a 3-dimensional thermal-wind imbalance vector, which is the curl of the body force vector, is introduced. By equating the material derivative of the 3-dimensional thermal-wind imbalance vector to zero, the C-vector equations in semigeostrophic and primitive systems are derived.
