## Baroclinic Instability In The Ocean

In our discussion of the general circulation of the ocean in Chapter 9 it was emphasized that the mean circulation emerges only after long time-averages. Instantaneously the flow is highly turbulent (see, e.g., Figs. 9.19 and 9.22) and the numerical simulation shown in Fig. 9.24. The sloping

9If h is the thickness of the layer across which the density changes by A a, then multiplying f /h by A a/prf we arrive at:

f_ AAa da h Pref Pref dz as h and Aa become small.

isopycnals evident in Fig. 9.7 suggest that there is available potential energy (APE) in the ocean's thermocline. Indeed, following the analysis of Section 8.3.2, the ratio of APE to kinetic energy in the flow is, from Eq. 8-11, of order (L/Lp)2. In the ocean the deformation radius, Eq. 7-23, has a value of Lp = NH/f ~ 5 x 10-3 s-1 x 103 m/10-4 s-1 = 50 km and so (L/Lp)2 ~ (1000 km/50 km)2 = 400 assuming that the mean flow changes over scales of 1000 km. Thus the potential energy stored up in the sloping density surfaces of the main thermocline represents a vast reservoir available to power the motion. This energy is tapped by baroclinic instability which fills the ocean with small-scale energetic eddies that often mask the mean flow. We can estimate expected eddy length scales and time scales using the arguments developed in Section 8.2.2 (see Eqs. 8-3 and 8-4). A deformation radius of 50 km yields eddy length scales of order 100 km. Growth rates are Teddy ~ Lp/U = 50km/10cms-1 = 5 x 105 s, a week or so, significantly slower than that of atmospheric weather patterns. Eddy lifetimes in the ocean are considerably longer than those of their atmospheric counterparts; weeks and months rather than the few days of a typical weather system.

The mechanism by which APE is built up in the ocean is very different from the atmosphere and, as we now describe, involves the collusion of mechanical (wind) and thermodynamic processes. In our discussion of the atmospheric general circulation in Section 8.3, we described how the net radiative imbalance led to warming in the tropics, cooling over the pole and hence the equator-to-pole tilt of 9 surfaces and a store of available potential energy which can power the eddy field. In contrast, horizontal density gradients in the interior of the ocean and their associated store of APE are produced mechanically, by the same processes that drive the wind-driven currents, as illustrated in Fig. 10.25 . In the anticyclonic gyre, on the equatorward flank of the Gulf Stream, for example, Ekman pumping depresses isopycnals and isotherms by pumping light, warm water downward; poleward of the Gulf Stream, where the curl of the wind stress is cyclonic and there is a cyclonic gyre, Ekman suction lifts up the isopyc-nals and isotherms, as we saw in Fig. 10.11. Thus a horizontal density and temperature

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