Name_______________________________________
Due October 25th
Homework 4
1) Barnegat Bay is a shallow coastal lagoon orientated in the North/South direction
along the New Jersey coast. The mean depth of the bay is approximately 2m and
approximately 50 km long and 5 km wide. The fluid in the bay is initially at rest but
is then subject to a 10 m/s wind from the south.
A) Neglecting the Coriolis acceleration describe how the terms in the depth
averaged momentum equation would evolve in time and how the depth
averaged flow would evolve in time.
B) Assuming that after a period of time the wind stress is balanced by an along
channel pressure gradient associated with the sea-level slope, what is the
elevation difference between the north end and south ends of the bay?
C) Assuming a velocity scale whereby the current speed is 3% of the wind
speed, estimate how long it would take to reach the steady state in 2. Hint:
Use the continuity equation to estimate the time rate of change of sea-level
and assume that the flow at the ends of the bay is zero (because of the
boundary).
D) How would the inclusion of the Coriolis acceleration alter the evolution of the
flow and sea-level field?
2) Ponder these problems using conservation of potential vorticity
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?
iii. To the east and west of this location the water depth decreases
by a factor of two. Describe how the relative vorticity changes
for each case as these currents flow over this shoaling
topography.