Vertical Structure: Baroclinic Quasi-Geostrophic Models

Abstract

Observations of the general circulation of the oceans, described briefly in Chapter 1, show that the most vigorous motion, driven primarily by the wind, takes place in the upper 1–2 km of the ocean and then diminishes dramatically with depth. Although it is difficult to obtain reliable measurements of time-averaged velocity in the midocean because of the presence of fluctuations on time scales of months, the signature of this intensification of the velocity field near the upper boundary of the ocean is evident in the more easily observed density field of the oceans. The thermal wind relation (see below) relates the vertical shear of the horizontal velocity to the horizontal density gradient. Therefore regions of sharp density variations horizontally can be identified as regions of strong currents. Figure 3.1.1, taken from the Levitus Atlas (1982), shows a zonal average of the density field in the Atlantic Ocean. The region of strong density gradient is seen to be limited to the upper ocean. The horizontal and vertical density gradients are captured largely in the upper 1 km and diminish sharply with depth. This phenomenon of the rapid drop-off with depth of the motion and the associated variations of the density field presents us with a theoretical problem which is fundamental to our understanding of the dynamics of the ocean, while being at the same time of considerable difficulty. The link between the density field and the velocity means that the problem of explaining the observed oceanic density field is nothing less than the problem of explaining the full three-dimensional structure of the oceanic circulation.