Assignment 5 (45 pts)
Name:____________________________
1a. (5 pts) Show that the linear form of the seawater density function,
 T , S , p    o 1   T T  To   S S  S o  K p  po , can be represented in exact
differential form as
d 0   0T dT  0  S dS  0 KdP
b. (10 pts) In the mid-latitudes, the pycnocline is approximately located at a depth of 500
to 1000 m.
depth
500 m
1000 m
density
The average value of seawater density at 500m is o  1025 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
K ~ 4.5  10 6 dbar 1 , respectively.
In the mid-latitudes, the temperature decreases approximately 10 o C per 500 m, the
halocline decreases 2 PSUs per 500 m, and pressure increases in accordance with the
hydrostatic approximation, p   0 gz . Find the changes in density due to each of the
above individual gradients as well as the net change in density over the pycnocline.
2. (5 pts) If a fluid parcel in Question 1 is displaced from 500 m to 1000 m, describe the
thermodynamic process(es) that govern heat transfer between it and the surrounding
environment.
3. The following image is an idealized density
profile taken from http://www.windows.
ucar.edu/earth/Water/images/sm_density_depth.jp
g
a) (5 pts) Find the stability
1 d
parameter E  
for this
 dz
density profile.
b) (5 pts) Is it appropriate to assume the form E  
1 d
to calculate the stability
 dz
parameter E in part a? Explain your answer.
4. (5 pts) Provided the water column is stable in question 2, calculate the buoyancy
frequency in the pycnocline.
5. (5 pts) a. Density of air at standard atmospheric temperature (0°C), composition (78%
nitrogen, 21% oxygen, and 1% argon), and pressure (1013.25 mb) has been roughly
estimated to be 1.2925 kg m3 . Determine which has the greater impact on air density:
heating the air to 20°C, or adding 26 g kg 1 of water vapor to the air. State any
assumptions you make.
b. (5 pts) Does the sensitivity of density to temperature and water vapor examined in part
(a) change if the starting position is T=20°C (instead of T=0°C)? Explain your answer.