Dynamic adjustment refers to the simultaneous changing of the pressure and velocity fields of a large-scale flow from an initially unbalanced state to a new balanced state. The conceptual issues concerning such adjustment are discussed in Section 7.1. In Sections 7.2 and 7.3, we solve the adjustment problem for two canonical forms of initial unbalanced disturbance in the context of a shallow-water model: a disturbance that has a velocity field without pressure variations or vice versa. We show that the new balanced state can be deduced without having to work out the transient evolution by virtue of conservation of potential vorticity in each fluid column. The analytic solutions reveal that whether the mass field or the velocity field would do most of the adjustment depends strongly on the scale of the initial disturbance. An extension of the geostrophic adjustment analysis to a gradient-wind adjustment analysis is finally discussed in Section 7.4.

Problem of rotational adjustment

From the perspective of large-scale geophysical flow, dynamic adjustment is synonymous with rotational adjustment, which is a generic term for the process of establishing a near-balance state from an imbalanced state in a rotating fluid. The observed large-scale wind vectors everywhere on an upper-level isobaric surface in mid-latitude are always approximately parallel to the height contours as evidenced in Fig. 2.5. In other words, a geostrophic balance between the wind field and the pressure field appears to be prevalent all the time.