PO Problem Set 8
Name___________________________ Due November 9th .
1) The figure below depicts a two layered ocean with the interface sloping down a total of 500 meters between point A and point B which is 50 km to the east. The sea level is also tilted, but this slope is unperceivable in this schematic. The flow is geostrophic and is equal to 1 m/s in both layers. However in one layer the flow is to the north while in the other layer the flow is to the south. The lower layer density is not given, but it is greater than the density of the upper layer. The Corilos frequency is 10-4 s-1.
A) Which layer is flowing to the north (into) and which layer is flowing to the south (out of)? Explain your reasoning (Hint—based on the slope of the interface you should be able to figure out the sign of the shear and thus which layer is flowing which way)
B) What is the sea-level difference between points A and B? Which point is higher?
C) What is the density of the lower layer? (Hint: take the difference between a momentum equation in the upper layer and one for the lower layer. Note that the pressure gradient in the upper layer is only due to the surface slope, while the pressure gradient in the lower layer contains contribution from both the sea level slope and the interface slope)
2) The panel to the right depicts a hypothetical latitudinal variation in the east/west wind stress. The stress is modeled as
.1* sin (latitude/10)
and there is no wind stress in the north/south direction.
a) Assuming that he Coriolis frequency is constant (f plane) and equal to 10-4. Derive an expression for the vertical motion at the base of the Ekman layer as a function of latitude.
b) Now assume that this wind stress field occurs on a Beta plane, draw a schematic showing the structure of the ocean gyres that this wind field would drive. What are the latitudes that separate ocean gyres?
c) c) Still using the beta plain approximation derivative the expression for the north/south mass transport. What is the relationship between the maximum and minimum north/south transports and the wind stress curl?
3) List in order your top three choices for a topic for the student presentation (Dec 4th). While we encourage you to discuss an ocean current, you may choose other topics. If you need help please contact Jim Miller or Bob Chant.