Assignment 2 (35 pts)
Names:____________________________ ______________________________
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1. (15 pts) The linear form of the seawater density function is
 T , S , p    o 1   T T  To    S S  S o   K  p  po  , which can be represented in
exact differential form as
  0  d 0   0T dT  0  S dS  0 KdP
In the tropics, the pycnocline is located at an approximate depth of 800m with a thickness
of about 400m (Gnanadesikan, de Boer, and Mignone, 2007).
depth
600m
1000m
density
kg
.
m3
Standard values for the thermal expansion, haline contraction and isothermal
compressibility coefficient coefficients are  T ~ 2  10 4 K 1 ,  S ~ 3  10 4 psu 1 and
The average value of seawater density at 600m is  o  1027
K ~ 4.5  10 6 dbar 1 .
In the tropics, the temperature decreases approximately 10 o C per 500m; salinity in the
halocline decreases 2 PSUs per 500m, and pressure increases in accordance with the
hydrostatic approximation, p  0 gz . Find the incremental changes in density over the
pycnocline due to each of the above individual terms (temperature, salinity, and
pressure).
2. The following image is an idealized density profile taken from
http://www.windows.ucar.edu/earth/Water/images/sm_density_depth.jpg
a) (5 pts) Find the stability parameter E  
1 d
for this density profile.
 dz
b) (5 pts) Is it appropriate to assume the form E  
parameter in part a? Explain your answer.
1 d
to calculate the stability
 dz
3. (5 pts) What sort of thermodynamic process is assumed to occur between the fluid
parcel and surrounding environment in your calculation in question 2?
4. (5 pts) Provided the water column is stable in question 2, calculate the buoyancy
frequency in the pycnocline.