where we have set pi/p2 —► 1 and used Eq. 7-23 to express the result in terms of the deformation radius Lp.

Equation 8-11 is a rather general result for balanced flows—the ratio of APE to KE is proportional to the square of the ratio of L, the lateral scale over which the flow changes, to the deformation radius Lp. Typically, on the largescale, L is considerably larger than Lp, and so the potential energy stored in the sloping density surfaces greatly exceeds the kinetic energy associated with the thermal wind current in balance with it. For example, T varies on horizontal scales of L ~ 5000 km in Fig. 5.7. In Section 8.2.2 we estimated that Lp ~ 700 km; thus (L/Lp )2 ~ 50. This has important implications for atmospheric and (as we shall see in Chapter 10) oceanic circulation.8

8In fact in the ocean (L/Lp) ~ 400, telling us that the available potential energy stored in the main thermocline exceeds the kinetic energy associated with ocean currents by a factor of 400. (See Section 10.5.)

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