Physical Oceanography
Problems 6 and 7
Due October 1, 2014
Problem 6. Suppose you are in an ocean region where the density is constant
everywhere, and a pressure gradient occurs because the sea surface slopes
upward to the south at a rate of 2 cm for every 3 km.
a) Calculate the horizontal acceleration on a parcel of fluid.
b) How fast and in what direction will a parcel of fluid initially at rest be moving
after 100,000 seconds? Assume the only force present is the pressure gradient
force.
c) Suppose the sea surface is as above, but there is also a second layer below
whose density is 3 kg m-3 greater than the surface layer, and the interface
between the two layers slopes downward to the south. Suppose at some depth
H the pressure gradient between two points a distance L apart is equal to zero.
How much larger is the slope of the interface between the two layers than the
slope of the sea surface?
Problem 7.
(a) Suppose you pass a football 100m along a straight line parallel to the
sidelines in Rutgers stadium. Assuming it travels at a constant speed, how long
would it have to travel to be deflected 4cm to the right of it’s direction of motion
by the Coriolis force?
(b) If you did the same thing at a stadium in Fairbanks, Alaska, how long would it
take?
(c) If in addition to the pressure gradient caused by the slope of the sea surface
in problem 6 a and b (constant density case) there is a Coriolis force with f = 10-4
s-1 what is the direction and magnitude of the current? Assume steady state and
the only forces are the pressure gradient and Coriolis force.