flux drifts to lower latitudes with the deepening of the mixed layer depth at lower latitudes (Fig. 5.196c).
On the other hand, the upwelling rate at the base of the mixed layer at mid and high latitudes for the case with the deepest mixed layer h = H (0.7y + 0.3) is the lowest, although it is the highest near the southern boundary (Fig. 5.197a). Similarly, the energy required for sustaining the subsurface diapycnal mixing is the lowest at mid and high latitudes, and the corresponding meridionally accumulated energy for sustaining subsurface diapycnal mixing is the smallest among all three cases (Fig. 5.197b, c).
In contrast, for the case with a shallow mixed layer at lower latitudes, h = H (0.9y + 0.1), the MOC transports less water and heat; at the same time the circulation may require more energy for sustaining the subsurface diapycnal mixing, as shown in Figures 5.196 and 5.197.
Thus, these three cases demonstrate that, with a deep mixed layer at lower latitudes, the meridional overturning cell can transport more water at low and mid latitudes, and more heat poleward. At the same time, the circulation may require less mechanical energy for sustaining diapycnal mixing in the ocean interior.
Results obtained from an oceanic general circulation model The analytical model discussed above is for a highly-simplified two-dimensional model. Similar results can be obtained from numerical experiments based on an OGCM. In most existing models, wind energy input to the mixed layer is parameterized in terms of energy input to the turbulence using simple formulae. For example, wind energy input can be parameterized as e = pm * u*3 (5.427)
where m* is an empirical constant in nondimensional units, and u* is the (atmospheric-side) frictional velocity.
The dynamical impact of wind stress to the surface ocean is complicated. Obviously, the contribution of wind energy input to the ocean should include contributions from a wide spectrum in space and time; thus, a simple formula such as Eqn. (5.427) is unlikely to convey the complete information about energy transport from the atmosphere to the ocean.
In OGCMs m* is usually set to 1.25. However, a quite different value of m* has also been used in previous studies. Noh et al. (2004) estimated turbulent kinetic energy at the surface with m* = 1.40; but m* was taken to be 3.50 in the study of Craig and Banner (1994). (The air-side frictional velocity is used here, so that there is a coefficient of about 28.6 in the formula in our calculation, compared with that used in the studies using the water-side frictional velocity.) However, Stacey (1999) analyzed data from the Knight Inlet in southwestern Canada, and concluded that using m* = 5.25 provided the best fit to the data.
In the following experiments, the model was spun up from a state of rest for 1,000 years, in which m* was set to 1.25. Based on this run, five experiments were then run for 400 years, in which m* was set to 0.4, 1.25, 3.75, 7.5, and 12.5. The experiment with m* = 1.25 is taken as the standard case in this study. A higher value of m* implies that a larger amount of wind energy input is used to deepen the mixed layer depth under the same wind stress.
The basic idea behind this approach is as follows. The contributions of wind stress to the oceanic circulation are rather complicated, but at least they can be separated into two categories: the large-scale mean wind stress, which drives the Ekman transport and the wind-driven gyre in the upper ocean, and the source for the turbulent kinetic energy in the upper ocean. Simply changing the "mean" wind stress profile in the ocean model cannot represent the complicated contribution from wind accurately. As a compromise in our conceptual study here, we choose to alternate this single parameter m* to simulate contributions to surface turbulence in the upper ocean from the wind stress components with relatively high spatial and temporal resolution.
An increase in m* has the profound effect of mixed layer deepening at low and mid latitudes, where mixed layer depth is primarily controlled by the turbulence kinetic energy input from the winds Fig. 5.198a). It is generally accepted that increasing m* can increase the mixed layer depth in the bulk mixed-layer model (Gaspar, 1988). Since a bulk mixed-layer model is used in this study, choosing a high value of m* may lead to a deep mixed layer depth.
An immediate consequence of a deeper mixed layer at low and mid latitudes is the increase in the meridional pressure gradient in the upper ocean; this leads to an intensification of the MOC. For example, when m* = 7.5, the MOC increases to nearly 1.6 Sv, compared to the case with m* = 1.25 for the latitudinal bands of 20-45° N (Fig. 5.198b).
Due to the increase in the meridional mass transport, the circulation can carry more heat poleward. In fact, the maximal poleward heat flux increases from 0.38 PW for the case of m* = 1.25, to 0.57 PW for the case of m* = 7.5 (Fig. 5.199a).
In terms of mechanical energy balance, diapycnal mixing in the ocean interior is controlled by mechanical energy input from the winds and tides (Munk and Wunsch, 1998; Huang, 1999). A larger amount of mechanical energy input can result in stronger diapycnal mixing in
Mixed layer depth (m)
Overturning rate (Sv)
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