Post-class Homework assignment 1. Due on Sept. 17th, at the beginning of the class.
1. Read chapter 1 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: For the rest of the course note, I will ask you to do the same exercise as part of the
corresponding pre-class home work assignment.
NOTE4: 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 show me your answers.
Q1. What is the definition of 'water parcels'? Is there a typical size of water parcels? Is there any
connection between water parcel size(s) and resolutions of numerical flow simulations?
Q2. What are the characteristics of the ocean listed in the course note and the typical sizes associated
with them (if mentioned)?
Q3. True or False
-The scales of the forces involved in ocean physical phenomena are always weak.
-Ocean phenomena come in many different time scales and sizes.
-Molecular dynamics is infeasible for describing currents in the ocean even though this may be the
most accurate way.
-Navier-Stokes equation describes motion of a molecule.
-Navier-Stokes equation describes collective motion of molecules.
-Navier-Stokes equation is a relationship between forces, mass, and acceleration.
-The Coriolis force acting on a missile is smaller than that on a water parcel in an ocean current.
-Radio waves and light do not penetrate water much.
-The 'weather' of the ocean (such as pressure, temperature, currents) changes 10 times slower than that
of the atmosphere (50 days instead of 5 days), and the spatial pattern of the ocean 'weather' is 10 times
smaller than in the atmosphere.
-Exchange of chemicals between different depths of the ocean is suppressed by stable stratification.
-Stable Stratification can support “internal” waves, breaking of which enhances exchange of chemicals
between different depths of ocean.
-Horizontal density variation gives rise to currents.
-In many large scale ocean and atmospheric phenomena, effects of the Coriolis force are visible. This is
because the other forces involved for these phenomena are very weak compared to the Coriolis force.
Q4. Fill the blanks below. (The blanks are shown by underline dots.)
What factors do you need to think about when you consider ocean currents?
Tips:
You should look at the figures below as well as your lecture slides and course note.
In the future, I may ask you the WHY-part more often than the WHAT-part. So you should pay
attention to the WHY-part too.
WHAT: ....................
WHY: The governing equations of the dynamics of the ocean are designed to describe all the
phenomena that can happen in the ocean (See the first figure below). Hence they have too many
solutions to them and finding a particular solution is beyond our capability. One way to overcome this
problem is done by considering this. By knowing this, you can tune the governing equations to the
physical phenomena of your interest and eliminate the solutions for other physical phenomenas
beforehand.
Also knowing this is necessary to analyze your data and find noise and aliasing or to prevent losing
your measuring instruments.
WHAT: ..................
WHY: This blocks or steer ocean currents by its existence. This reflects ocean waves.
This makes the flows of spatially large scale physical phenomena almost 2 dimensional; That is to say,
horizontally ocean is large so that it can accommodate large scale structures, but there is not much
space to accommodate vertically large structures. So large structures can exist only in the horizontal 2
dimensions. Also this drags the ocean currents at its horizontal and lower boundaries.
WHAT: Stratification
WHY: .........................
WHAT: ...............
WHY: This not only accelerates any velocity in the direction perpendicular to its current velocity but
also sustains a flow when there is a horizontal density gradient.
WHAT: ................
WHY: The energy from the sun produce pressure gradients (by making warm and cool parts on earth)
and hence give birth to This. This drags the ocean from its upper boundary and cause boundary-layer
circulations like Langmuir circulations and the Ekman transport. Moreover, this drag can drive the big
gyres too.
WHAT: ................
WHY: Again the energy from the sun causes precipitation, evaporation, and heat inputs to the ocean
and hence gives birth to this. The principal is simple: The heavy stuff sinks and the light stuff floats.
The potential energy stored in the ocean in this form can drive its global scale circulation. This is why
some water deep in the ocean flowing at low latitudes sometimes is from polar regions.
WHAT: ..................
WHY: This competes with stratification. Without this, some ocean surface will boil and the ocean floor
will almost freeze. Fish will die because the ocean will be hypoxic. The number one producer of this is
winds, but turbulence and molecular motions can also produce this (though much less).
Is there anything else?
This is Fig 1.7 of 'Introduction to Geophysical Fluid Dynamics' by B. Cushman-Roisin and J-M.
Beckers.
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