## Westward drift

In this section, we give a slightly different explication of why the boundary current is in the west. It is not really a different explanation because the cause is still differential rotation, but here we think about it quite differently. We'll see that the effect of differential rotation is to make patterns propagate to the west, and hence the response to the wind's forcing piles us in the west and produces a boundary current there.

We noted already that the component of Earth's rotation in the local vertical direction also increases as we move northward or, putting it a little informally, the spin increases northward. (The spin is also called the vortic-ity.) Now consider a parcel of fluid sitting in the ocean. It may be spinning from two causes, namely, because it is spinning relative to Earth and because Earth itself is spinning. If that parcel moves and if no external forces act upon it, then the total spin of the fluid parcel is preserved. Its local spin relative to Earth must therefore change to compensate for changes in Earth's spin.

Let's now imagine a line of parcels, as illustrated in figure 4.5. Suppose we displace parcel A northward.

Figure 4.5. If parcel A is displaced northward, then its clockwise spin increases, causing the northward displacement of parcels that are to the west of A. A similar phenomenon occurs if parcel B is displaced south. Thus, the initial pattern of displacement propagates westward.

Because Earth's spin is counterclockwise (looking down on the North Pole) and this spin increases as the parcel moves northward, then the parcel must spin more in a clockwise direction to preserve its total spin. This spin has the effect of moving the fluid that is just to the west of the original parcel northward, and then this fluid spins more clockwise, moving the fluid to its left northward, and so on. The northward displacement thus propagates westward, whereas parcels to the east of the original displacement are returned to their original position so that there is no systematic propagation to the east. Similarly, a parcel that is displaced southward (parcel B) also causes the pattern to move westward. This is an idealized example—in fact we have just described the westward propagation of a simple Rossby wave—but the same effect occurs with more complex patterns and in particular, with the gyre as a whole. Thus, imagine that an east-west symmetric gyre is set up, as in the left panel of figure 4.3, with the winds and friction in equilibrium. Differential rotation then tries to move the pattern westward, but of course the entire pattern cannot move to the west because there is a coastline in the way! The gyre thus squishes up against the western boundary in the manner illustrated in the right panel figure 4.3, creating an intense western boundary current. This way of viewing the matter serves to emphasize that it is not the fric-tional effects that cause western intensification; rather, frictional effects allow the flow to come into equilibrium with an intense western boundary current, with the ultimate cause being the westward propagation caused by differential rotation.

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