L

Longitude

Fig. 5.103 The Goldsbrough-Stommel circulation of the world's oceans, neglecting the inter-basin transport. Each arrow indicates the horizontal mass flux integrated over a 5° x 5° box, in Sv; along the western boundary of each basin, there is a curve indicating the northward mass flux (in 106 m3/s) within the western boundary, which is required to close the circulation (Huang and Schmitt, 1993).

evaporation and precipitation. The western boundary currents that perform the role of closing the meridional mass flux at each latitude in each basin are then attached to the interior solution.

Baroclinic haline circulation in the oceans The circulation discussed above is only the barotropic component of the saline circulation, which is tiny compared with the wind-driven circulation and the thermal circulation in the oceans. As discussed above, the Goldsbrough-Stommel circulation has volume flux on the order of 1 Sv, but wind-driven circulation is on the order of tens of Sverdrups.

For a long time, the Goldsbrough-Stommel circulation was treated as an abstract theoretical idea not directly linked to the oceanic general circulation and thus not particularly useful for practical application. A close examination reveals, however, that the Goldsbrough-Stommel circulation is only one aspect of the circulation related to freshwater flux across the air-sea interface. It turns out that the Goldsbrough-Stommel circulation is only the barotropic component of the circulation induced by the air-sea freshwater flux. If there were no salt in the ocean, the Goldsbrough-Stommel circulation would be the only circulation induced by the freshwater flux. Within another theoretical limit of no external mechanical energy (either from wind stress or tidal flow) available for sustaining diapy-cnal mixing, there would be no baroclinic component of the haline circulation; thus, the Goldsbrough-Stommel circulation would be the only possible circulation induced by the air-sea freshwater flux.

There is no salinity involved in the dynamical analysis presented above. However, if salinity and salinity mixing driven by external sources of mechanical energy are included, the entire picture will be totally different, because baroclinic circulation associated with salt mixing and transportation as strong as the wind-driven circulation or the thermal circulation will be developed, as discussed in the next section.

To understand the baroclinic haline circulation, we begin with the circulation in an estuary. Estuaries are the interface between the freshwater-dominated river flow and the saltwater-dominated oceanic circulation. Water from the river upstream provides the freshwater input, and the open ocean provides the downstream condition.

Freshwater-flux-induced circulation in a salty estuary

The circulation in an estuary depends on many factors, such as the amount of river run-off, the mean salinity, and tidal mixing. In the estuary, freshwater from river run-off overlies the salty water from the open ocean; thus, there is a strong stratification, which is mostly due to the salinity difference. As discussed in Chapter 3, diapycnal mixing in such a strongly stratified environment requires an external source of mechanical energy, from tides and wind.

If there were no external mechanical energy available for sustaining vertical mixing, the freshwater from river run-off would flow over the salty water in the estuary. As a result, the only circulation would be movement of the top layer, and the lower layer below would be stagnant. Since there is no mixing, the volume flux in the upper layer remains constant over the whole path through the estuary. There is no salt in the upper layer, so water there remains fresh; the salinity of the lower layer remains the same as in the open ocean, which we take as 35 (Fig. 5.104a). However, with tidal mixing, a small amount of river run-off can induce a huge return flow in an estuary (Fig. 5.104b). In the discussion in this section we will assume that there is always an energy source available for mixing, such as the barotropic and internal tides, internal waves, wind stress, and other sources; however, the exact nature of the energy source is not our concern here.

The North Atlantic Ocean as an estuary

Similar to the case discussed above, the North Atlantic Ocean can be treated as a huge estuary, with evaporation at low latitudes and precipitation at high latitudes that exactly balance each other. First, let us assume that there is no external mechanical energy available for sustaining mixing; thus diapycnal diffusivity is zero. At time t = 0, evaporation starts at low latitudes and rain starts to come into the subpolar basin. Precipitation at high latitudes builds up the free surface, and water starts to flow toward low latitudes (rotation would modify the path). At low latitudes, in the beginning, evaporation would make some water saltier and sink to depth, and this would give rise to motion in the salty water. However, as freshwater arrives at the low latitudes and gradually covers up the entire upper surface of the basin, evaporation can affect only the freshwater, but not the salty water. As the residual motions in the deep water gradually lose their kinetic energy, the only motion remaining

No vertical mixing

With vertical mixing

No vertical mixing

With vertical mixing

Deep Ocean Circulation Model
Fig. 5.104 Sketch of models with freshwater-driven circulation in an estuary and an open ocean: a, c model without vertical mixing; b, d model with vertical mixing.

will be the equatorward flow of freshwater on top of the stagnant deep and salty water (Fig. 5.104c).

Second, if there is external mechanical energy available for sustaining vertical mixing, there will be a very strong return flow induced by vertical mixing (Fig. 5.104d). Through salt conservation, the overturning rate is related to the salinity difference between the upper and lower layers of the ocean

Because AS is much smaller than So, a small amount of precipitation can induce a strong meridional circulation.

Haline circulation induced by freshwater flux is a complicated system, and the most convenient way to examine such circulation is to use a numerical model. The model is a mass-conserving model with a free surface, with 2° x 2° resolution (4° N-64° N, AO = 60°) and AX = 60° wide in the zonal direction, subjected to a "linear" profile of E — P, as shown in Figure 5.105,

Haline circulation under freshwater forcing wG = 1 m/yr wG = 1 m/yr

Fig. 5.105 Meridional distribution of mass fluxes: E — P is the evaporation minus precipitation (in m/yr), Interior is the poleward mass flux in the interior, WBC is the mass flux of the western boundary current, Meridional transport is the total poleward mass flux; all these mass fluxes are in Sv.

Fig. 5.105 Meridional distribution of mass fluxes: E — P is the evaporation minus precipitation (in m/yr), Interior is the poleward mass flux in the interior, WBC is the mass flux of the western boundary current, Meridional transport is the total poleward mass flux; all these mass fluxes are in Sv.

The corresponding zonally integrated volume fluxes in the ocean interior, the whole basin, and the western boundary regime are

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