4. Consider the Atlantic Ocean to be a rectangular basin, centered on 35° N,
10This statement refers to the midlatitude eddies evident in the height variance maps, Fig. 9.19 (bottom). The near-equatorial eddies evident in the surface current variance maps, Fig. 9.22 (bottom), are produced by another mechanism.
of longitudinal width Lx = 5000 km and latitudinal width Ly = 3000 km.
The ocean is subjected to a zonal wind stress of the form r (y) = -TS cos ( (10-23)
where ts = 0.1Nm-2. Assume a constant value of p = df /dy appropriate to 35°N, and that the ocean has uniform density 1000 kg m-3.
(a) From the Sverdrup relation,
Eq. 10-17, determine the magnitude and spatial distribution of the depth-integrated meridional flow velocity in the interior of the ocean.
(b) Using the depth-integrated continuity equation, and assuming no flow at the eastern boundary of the ocean, determine the magnitude and spatial distribution of the depth-integrated zonal flow in the interior.
(c) If the return flow at the western boundary is confined to a width of 100 km, determine the depth-integrated flow in this boundary current.
(d) If the flow is confined to the top 500 m of the ocean (and is uniform with depth in this layer), determine the northward components of flow velocity in the interior, and in the western boundary current.
(e) Compute and sketch the pattern of Ekman pumping, Eq. 10-7, implied by the idealized wind pattern,
5. From your answer to Problem 4, determine the net volume flux at 35° N (the volume of water crossing this latitude in units of Sverdrups: Sv = 106 m3 s-1):
(a) for the entire ocean, excluding the western boundary current.
(b) for the western boundary current only.
(c) Assume again that the flow is confined to the top 500 m of the ocean. Determine the volume of the top 500 m of the ocean and, by dividing this number by the volume flux you calculated in part (a), come up with a timescale. Discuss what this timescale means.
(d) Assume now that the water in the western boundary current has a mean temperature of 20°C, whereas the rest of the ocean has a mean temperature of 5°C. Show that Hocean, the net flux of heat across 35° N, is
= PrefCpV AT , where V is the volume flux you calculated in part (c), and AT is the temperature difference between water in the ocean interior and in the western boundary current. Recall that Fig. 5.6 shows that the Earth's energy balance requires a poleward heat flux of around 5 x 1015 W. Calculate and discuss what contribution the Atlantic Ocean makes to this flux.
6. Describe how the design of the laboratory experiment sketched in Fig. 10.18 captures the essential mechanism behind the wind-driven ocean circulation. By comparing
Eq. 10-16 with Eq. 10-12, show that the slope of the bottom of the laboratory tank plays the role of the ^-effect: that is the bottom slope <—> (1/tan cp) (h/a), where h is the depth of the ocean and a is the radius of the Earth.
7. Imagine that the Earth was spinning in the opposite direction to the present.
(a) What would you expect the pattern of surface winds to look like, and why (read Chapter 8 again)?
(b) On what side (east or west) of the ocean basins would you expect to find boundary currents in the ocean, and why?
If you live in the southern hemisphere perhaps you are not scratching your head.
Use Sverdrup theory and the idea that only western boundary currents are allowed, to sketch the pattern of ocean currents you would expect to observe in the basin sketched on the right in which there is an island. Assume a wind pattern of the form sketched in the diagram.
9. Fig. 5.5 shows the observed net radiation at the top of the atmosphere as a function of latitude. Taking this as a starting point, describe the chain of dynamical processes that leads to the existence of anticyclonic gyres in the upper subtropical oceans. Be sure to discuss the key physical mechanisms and constraints involved in each step.
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