Pre-class Homework for Chapter 2. Part 1. Due on Sep. 14th 2009, Noon
1. Read chapter 2 page 11-18 of the course notes. Mark all the new words, their definitions, and newly
defined symbols with light green color. Mark all the theorems (i.e. something derived rather than
something defined.) with yellow color. Mark all the defining conditions/assumptions made to derive the
theorems with deep green. Mark the most important points/equations of the chapter with orange. Mark
the part you found very informative for you with blue.
NOTE1: You can choose different colors if you like. Just stick to one color for one meaning so that you
can quickly review your notes in the future. i.e. You know what color to look for when you are looking
for something. Once you decide the colors, don't ever change them in your lifetime.
NOTE2: The purpose of this exercise is that you consciously identify and differentiate these items.
Identification and differentiation of these items are something that you should do whenever reading any
scientific paper or book. Coloring is just one method to do this. If you prefer any other method, do use
that method instead of coloring.
NOTE3: You don't need to show me your work for this part because you do this for your own benefit.
2. Answer the following questions and send me your answers via email (nsuzuki@gso.uri.edu)
Q1. 1N = 1 kg m/s2 and is a unit of force. True or False?
Q2. 1 Pa = 1Nm-1 and is a unit of pressure. True or False?
Q3. 10-5 bar = 1Pa and is a unit of pressure. True or False?
Q4. 1dbar = 104 Pa = 10000 kg m-1s-2 . True or False?
Q5. I have water in a column container whose bottom area, A, is 1m2. The total mass of the water, M,
is about 1000kg. The water is not moving.
- Q5-1. What is the depth of the water?
- Q5-2. What is the net force acting on the bottom of the container in terms of A, M, and g where g is
the gravitational acceleration?
- Q5-3. Pressure is defined as force per unit area. What is the pressure at the bottom of the container in
terms of A, M, and g?
- Q5-4. Is the pressure at the bottom about 1dbar?
Q6. The pressure at the bottom of 1m depth water column, when the water is vertically accelerating, is
about 1dbar. True or False?
Q7. Horizontal pressure gradient across Gulf Stream is O(10-1 Pa/m) and the vertical pressure gradient
is O(104 Pa/m). True or False?
Q8. Horizontal density gradient causes horizontal pressure gradient and the horizontal pressure
gradient can drive a flow. True or False?
Q9. Temperature and salinity gradient affect the ocean currents because it causes density gradients and
hence the corresponding pressure gradients. True or False?
Q10. When ocean is stably stratified, hypoxia may occur more often. True or False?
Q11. What is a chunk of water which shares the same temperature and chemical compositions called?
Q12. Why can one trace water masses using tracers even though they actually diffuse?
Q13. How come oxygen does not affect the dynamics of the ocean?
Q14. In-situ temperature in the ocean is about ................
Q15. 75% of the ocean is between ................
Q16. Horizontal SST distribution is roughly zonal. True or False?
Q17. What is a wind-mixed layer?
Q18. What is the thermocline?
Q19. What are the main, seasonal, and diurnal thermocline?
Q20. It is hard to mix water at a region in the thermocline.
Q21. Is the temperature pattern above the main thermocline zonal?
Q22. Is the temperature pattern below the main thermocline zonal?
Q23. Fill the blanks with enforces/breaks. Wind ........... the stratification and sun light .......... the
stratification.
Q24. Fill the blanks with summer/winter. In many temperate regions, there is stronger heating and
weaker winds in .......... and weaker heating and stranger winds in .......... .
Q25. Let the salinity of the ocean be constant. Then the in-situ temperature of a neutrally stable
stratification goes up with depth. True or false?
Q26. Let the salinity of the ocean be constant. Then the potential temperature of a neutrally stable
stratification goes up with depth. True or false?
Q27. Fill the blank. Let the salinity of the ocean be constant. If the vertical profile of the potential
temperature goes down, then its stability is ............ .
Q28. θ4 is the temperature that the parcel of water would have if it were transported to the depth at
where the pressure is 4000dbar (, which is about 4000m depth). True or false?
Q29. Suppose you are poor. You have a room and a bicycle pump and that's everything you have. You
are room is hot and you want to cool it down. Can you do it just by using the bicycle pump?
3. This part is solely for our (the teachers) information. Not graded.
Please tell me what part of the reading material you want the teacher to spend time and explain more
during the lecture? Please list any questions you have.
SOMETHING TO THINK ABOUT 1: (I just want you to think about this. You don't need to write
down any answer for this. You can discuss this in class or with your friends though.)
Look at Fig.2.2 on page 14 Chapter 2. Why is the temperature profile of the thermocline not linear?
Note: The conduction of (or diffusion of) temperature is proportional to its gradient ∂ T/∂ z.
Thus, when there is no temperature flux by advection (i.e. no ocean currents), the governing equation
of the temperature is ∂ T/∂ t = ∂ ( k ∂ T/∂ z) / ∂ z with a constant of proportionality k. The steady
solution for this equation is linear T(z) = az+b. In order to have a non-zero temperature gradient
(i.e. a ≠0), there must be a constant heat incoming flux from the top of the thermocline and the same
amount of heat loss at the bottom of the thermocline like the figure below.
T
0
Heat flux due to sun light
z
Heat reservoir / Sink of heat
So what are the reasons that the temperature profile is not linear? Some possibilities are:
- k may not be constant???
- Maybe advection is the key???
- A non-steady solution of the above equation is
T(t,z)= A exp( t + (z - zbottom)/ sqrt(k) ) + B exp( t - (z - zbottom)/ sqrt(k) ) + C.
This has a exponential form but this solution does not satisfy, many boundary conditions and initial
conditions???
- The light penetration is exponential decay. But the penetration depth may be too short to explain
this???
SOMETHING TO THINK ABOUT 2:
The surface waters in polar regions are cooler (in the senses of annual mean) than the deeper waters.
Where do the deeper waters get their heat from?