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0 50 100 150 200 250 300 350 Day is quickly lost to the convective adjustment during the winter season. This seasonal cycle reinforces the basic idea that cooling on the surface does not create mechanical energy; it can transfer GPE to KE only.

3.7.4 Balance of GPE/AGPE during the adjustment of circulations

GPE and its balance are one of the most important aspects of the oceanic circulation theory. Discussions in previous sections have been focused on the balance of GPE and the spatial distribution of AGPE for steady circulations. At shorter time scales the oceanic circulation, including GPE and AGPE, may undergo a transition. In particular, the total amount of mechanical energy may change with time, i.e., sources and sinks are not in exact balance all the time. This is, in some ways, much like the oxygen deficit experienced during a short-distance run. You run so fast that a large amount of oxygen is consumed, which is much larger than the amount of oxygen you can take in through breathing. As a result, your oxygen is unbalanced during the short duration of the run.

Similarly, for the oceanic circulation, a strong cooling at high latitudes on short time scales, such as interannual or decadal, can release a large amount of GPE and convert it to KE, thus giving rise to a strong circulation over a relatively short time scale. It is notable that the total amount of GPE of the mean state is not conserved for such short time scales because cooling does not create GPE or KE; instead, cooling can only release the large amount of GPE originally stored in the system and convert it to KE. Thus, strong circulation can be induced by strong cooling on decadal or shorter time scales, and such a strong circulation is not inconsistent with the theory of energetics of oceanic circulation.

In this section we discuss the balance of GPE and AGPE during a time evolution process of the circulation. This is also an area which has not received much attention so far. As an example, we examine the balance of GPE and AGPE for the case of a circulation with purely surface thermal forcing (i.e., without wind stress and freshwater flux).

The model is the same as used in Section 3.7.3 with a fixed vertical mixing coefficient of k = 0.3 x 10-4 m2/s. The model is subject to an upper surface relaxation condition, with a linear relaxation temperature profile; 25°C at the equator, linearly declining to 0°C at the northern boundary (60° N).

The model starts from an initial state of uniform temperature of 10°C, and runs for 5,000 years in order to reach a quasi-equilibrium. At the end of this spin-up process, the mean sea level is -1.70 m below the original level of z = 0. The drop of mean sea level in the model is due to the reduction of volume induced by cooling. Thereafter, the model is re-started at time t = 0 from the quasi-equilibrium state, and run for 2,000 years under two slightly different relaxation temperature profiles:

1. The Cooling Case: the surface relaxation temperature is 25°C at the equator and linearly declines to —2°C at the northern boundary (60° N).

2. The Warming Case: the surface relaxation temperature is 25°C at the equator and linearly declines to 2°C at the northern boundary (60° N).

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