Homework #9 Due October 27th
Name ______________________________________
1) Use the concept of the conservation of potential vorticity to answer the
following questions.
a) The Kuroshio current flows directly east from Japan. Assume that it has no
lateral shear (i.e. relative vorticity is zero). However after some interval the
current begins to meander with northward and southward meanders In
these meanders the stream develops a relative vorticity that is dominated by
the flow curvature (i.e. the sign of the relative vorticity is determined by the
curvature of the flow).
i. Draw a schematic of this current and note the sign of the
relative vorticity in the northward and southward meanders
ii. Assuming that the change in the absolute vorticity is
dominated by changes in relative vorticity how would the
thickness of the current change in northward and southward
meanders?
iii. How would the above answer be modified if variations in the
Coriolis frequency with latitude became important?
b) A current flows along a mid-latitude coast that runs east-west (i.e. f is
constant and equals 10-4 s-1) with the offshore direction to the south.
Shipboard observations one day show currents at the coast flowing 50 cm/s
to the east and linearly decrease to 0 cm/s 5 km offshore. However, on a
second day the currents at the coast are 50 cm/s to the west and again
decrease linearly to 0 cm/s 5 km from the coast.
i. Draw a schematic of these two scenarios and note the sign of
relative vorticity.
ii. What is the value of the relative and absolute vorticity in these
two cases?
2) The figure below depicts a schematic of the Gulf Stream where light warmwaters
are separated by cooler dense waters. Assume that the pressure gradient vanishes
below the front.
A
100 km
Sea Surface
B
Gulf Stream
Sargasso
r2 = 1027 kg/m3
1000 m
r2 = 1028 kg/m3
a) What is the elevation of the sea surface at point B relative to point A?
b) Estimate the transport in the Gulf stream based on your result in a. Give
your answer in Sv (106 m3/s)
c) How would the transport change if the depth of the lower layer remained
the same but the distance from A-B were only 50 km? (i.e. the slope of
the isopyncal has increased). Again assume that the pressure gradient
beneath the density interface is zero.
3) The Gulf Stream typically meanders north of Cape Hatteras and characterized by
a series of crests and troughs such as those labeled C and T on the sea-surface
temperature image below. Assuming that the change in total vorticity (f+ in the
Gulf stream is associated with the flow curvature in these meanders (i.e. the change
in the total vorticity is due to changes in only) discuss how the thickness of the
stream would vary at a crest vs. a trough using the principle of conservation of
potential vorticity.
4) Consider the two-layer systems depicted in diagrams 6a-d. Assume that the flow is
geostrophic and in the northern Hemisphere. Note the direction of the flows using a dot
for flow out of the page and an x inside a circle for flow into the page. If the flow is
unidirectional but vertically sheared note which flow is faster (15 points)
a
10 cm
c
10 cm
r1 = 1022 kg/m3
r1 = 1024 kg/m
b
10 cm
r1 = 1022 kg/m3
75 m
3
r1 = 1022 kg/m
10
d
r1 = 1022 kg/m3
r1 = 1022 kg/m3
50 m
75 m
r1 = 1024 kg/m3
r1 = 1024 kg/m3
75 m
3