Introduction to physical oceanography
EPS 131
(Fall 2005)
Instructor:
Eli Tziperman,
TF: Laure Zanna,
zanna@fas.harvard.edu, tel: 617-496-6361, office:
Geol. Mus. 101. office hours: Mon 2-3pm; section: Frid 2-3pm, Geol
Mus 103A.
Day, time & location: M-W-F 10:00-11:00
Location: Maxwell Dworkin G135
Announcements
Last updated: Jan 17, 2006
Take home final: please come pick up the exam from
outside of my office, museum building room 202b, Thursday Jan 19,
10am. it will be due 24 hours later at the same place. Allowed
material: only your class notes and all materials from the course
home page.
Laure will hold office hours on Monday 16th and Wednesday 18th
between 1 and 2pm.
Field trip to WHOI: Nov 9; visit to the
R/V
Atlantis
and the submersible
Alvin,
plus a tour in the labs of WHOI;
visit
schedule;
photos;

Feel free to write or call me with any questions:
Eli Tziperman; eli AT eps.harvard.edu
Office hours: call/ write.
Homework:
01,
02,
03,
04,
05,
06,
07,
08.
09.
10.
Laure's homework solutions:
01,
02
(and
this),
03,
04,
05,
06,
07,
08,
09,
10,
section lecture notes
What's the point of optional/ extra credit problems: apart
from the fun of doing them, they will count against homework
problems in which you may have missed an answer. . .
Matlab programs:
finite_diff_ex.m,
levitus94_temperature_profile.m,
phase_velocity2d.m,
pipe_1d_tracer.m,
ripples.m,
group vs phase, animated, Ian Eisenman
The movie competition! Particle motion in surface gravity
waves:
Ben&Eric,
Dave&Itay,
Doug&Ellen,
Saira&Atreyee,
VY,
Glenn,
Main ones:
- (Kn) J. A. Knauss, introduction to physical
oceanography, 2nd edition, 1996, Prentice Hall, Upper Saddle River,
New Jersey.
- (Ku) Kundo P.K. and Cohen I.M., Fluid mechanics. 2nd
edition 2002.
Also interesting:
- (St) Robert H. Stewart, on-line physical oceanography
book
http://oceanworld.tamu.edu/resources/ocng_textbook/contents.html
- on-line version of 'Regional oceanography'
http://www.es.flinders.edu.au/ mattom/regoc/pdfversion.html
- (OU) The open university team, ocean circulation, 2nd
ed, 2002.
- (OU-W)The open university team, waves, tides and
shallow water processes, 2nd ed, 2002.
Basic observations and theoretical understanding of ocean phenomena
from local surface beach waves to the effects of the oceans on global
climate. Observations and dynamics of ocean waves, currents,
turbulence, temperature and salinity distributions; Basic fluid
dynamics equations; the ocean's role in climate: wind-driven
circulation and the Gulf stream, thermohaline circulation and the
potential instability of Europe's climate, El Nino, the oceans and
global warming. A field trip to Cape Code and the Woods Hole
Oceanographic Institution.
Prerequisite: Mathematics 21 or Applied Mathematics 21, Physics 11 or
15 or equivalent, or permission of instructor.
(Somewhat more detailed lecture
notes, other
images and
supporting-material.)
- Outline and motivation.
lecture1
- Basics: Continuum hypothesis, pressure, hydrostatics
(Ku 1.4-1.5, p 4; 1.7 p 9-11). Kinematics: Eulerian vs
Lagrangian, material derivative (Ku 3.1-3.3 p 50-53).
Continuity equation (mass conservation, Kn, Box 4.1 p 69),
incompressible fluids. Stream line Ku 3.4, p 53-56),
stream function (Ku 3.13, p 69-70). Temperature and
salinity equations (conservation of heat and salt, Kn, end
of Box 4.1 p 70-71 and Box 4.2 p 74-75), molecular vs eddy mixing,
(stirring
animation
from
here).
Equation of state. Ocean: GEOSECS sections and typical
exponential temperature profile, the overturning ocean circulation
and the vertical temperature profile in the ocean (abyssal recipes).
Solar radiation, SW and LW absorption, earth energy balance, ocean
vs land heat capacity, air-sea heat flux components and geographic
distribution, meridional ocean heat flux (Kn p 39-61;
on-line figures from St sections 5.1,5.2,5.4,5.6,5.7 and
two heat-flux images from supporting material directory).
- Momentum equations: acceleration, pressure force, gravity,
friction, Coriolis force, wind stress (Kn, chapter 5, p
80-107; for Coriolis, a better source is Ku section 4.12 p
99-101); equation of state.
Ocean/ Atmosphere: The Boussinesq approximation
(Ku 4.18, p 117-119); scaling of continuity equation,
smallness of vertical velocity, and the hydrostatic balance as an
approximation to the z-momentum equation. Primitive equations.
Scaling of momentum equations, Rossby number
, and Ekman
number
; both are small for large-scale ocean flows, and
derivation of geostrophy (Kn p 110). Weather systems and
pressure highs and lows, ocean gyres and ocean surface height,
temperature/ density section across the Gulf Stream. Thermal wind
equations the problem of the ``level of no motion''; sea surface
height variation across the Gulf Stream.
- Density, sigma-t, potential temperature, potential density,
sigma-theta, sigma-4 (OU p 230-232); static stability;
Brunt Vaisala frequency (Kn p 29-34, 38) and
buoyancy oscillations;
T-S diagrams and mixing of two and three water masses (OU p
225-229); T, S geographic distributions (Kn p 163-183);
nonlinearity of eqn of state: sigma theta inversion for AABW
(Kn p 38 fig 2.9), cabbeling.
- Inertial oscillations (Kn p 108-109),
equations and circular trajectories of fluid parcels.
- Friction: molecular vs turbulent, horizontal vs vertical
friction in the ocean (Kn p 97-99, Fig 5.9); bottom
friction parameterization (Kn p 96-97); scale selective vs
non scale selective friction; inertial motions with horizontal
friction (Kn p 120);
- Combined effects of vertical friction, wind and rotation:
reminder: shear stress (Kn p 100), wind speed and wind
stress, balance of friction and rotation in mixed layer, Ekman
transport (Kn p 122-123); why don't icebergs move downwind?
Coastal upwelling; upwelling, nutrients, fisheries and El Nino
(OU p 133-137, 153-155);
- Ekman pumping (Kn p 125-128); Ekman spiral,
(Kn p 124); curl tau from observations; North Atlantic
subtropical and sub polar gyres;
- Mid term review: which terms in the Navier Stokes equations are
responsible for: inertial motions (
), damped inertial
motions (
), geostrophy (
), Ekman layers/ drift
(
), buoyancy oscillations (
), hydrostatic balance
(
). In temperature equation: abyssal recipes and
exponential temperature profile (
); vertical velocity being
so small (
).
- Effects of changes in Coriolis force and the general ocean
circulation: beta plane, f=f(y), beta=df/dy, beta v=f dw/dz;
Sverdrup balance (beta V = curl tau). Momentum and vorticity
equations for a simple linear, shallow water/ barotropic, time
dependent, bottom friction, rotating case (Kn p 128-131).
Vorticity examples: solid body rotation and f as a ``planetary
vorticity''; irrotational vortex (Ku p 125); Sverdrup
balance as a vorticity balance.
- Calculating the wind driven general circulation: Idealized ocean
basin and calculating v from the Sverdrup balance (and then
calculating u using mass conservation). The western boundary
current problem. Balance between friction and beta term: only
possible physical solution is at west. Heuristic vorticity
explanation of western boundary currents (Kn p 131-133;
OU, p 85-98).
- Surface ocean waves: (1) Qualitative phenomenology: wave
amplitude/ length/ number (scalar and vector)/ period/ frequency/
phase speed/ group speed; typical periods/ wave lengths of ocean
surface waves; particle trajectories (in deep, finite and shallow
water); scaling arguments for dispersion relation in deep/ shallow
water; refraction when approaching a curved beach; dispersive (deep)
and non-dispersive (shallow) waver waves; mechanism of breaking
waves; (2) Math (Kn 192-198): vector vorticity,
irrotational flow (vorticity=0, velocity=gradient of potential);
Bernoulli function and boundary conditions on velocity potential;
wave solution in 2d (x,z) (Kn p201, Table 9.1) and
dispersion relation; particle trajectories; phase and group
velocities (Kn 201-204); qualitatively again: phase and
grpu velocity in 2d, phase velocity is not a vector and its
components in (x,y) directions. Math again: phase shallow water
waves: shallow water momentum and continuity equations, wave
solution, dispersion relation; Tsunamis as shallow water waves,
waves refraction when approaching a curved beach.
- Other waves: Poincare (inertial-gravity) waves, coastal and
equatorial Kelvin waves, Rossby waves and a heuristic explanation of
westward propagation. Stratification, reduced gravity and internal
waves.
- Practicalities: using Matlab, solving a simple
advection-diffusion numerically: leap frog, center space
differencing, Robert Filter.
- El Nino:
- Thermohaline circulation: phenomenology, mean state, present-day
variability; different atmospheric response and surface boundary
conditions for Temperature and salinity; driving by T, breaking by
S; paleo climate perspective: introduction to paleo climate
variability, proxies, ice cores and sediment cores; THC during LGM,
possible variability during Heinrich and D/O events; advective
instability feedback; THC flushes; Stommel two box model and
multiple equilibria. Some misc slides that were presented in class
(only a few slides from each of these files):
1,
2,
3
Beginning texts:
- G. L. Pickard and W. J. Emery, Descriptive Physical Oceanography
- An Introduction, Butterworth Heinemann, 1990,
- Stephen Pond and George L. Pickard, Introductory dynamical
Oceanography, 3rd edition, Butterworth-Heinemann, 1993,
Intermediate texts:
- Philander, S. G. H., El Niño, La Niña, and the Southern
Oscillation., Academic Press, 1990,
- Benoit Cushman-Roisin, Introduction to geophysical fluid
dynamics, Prentice-Hall, 1995,
Advanced texts:
- Pedlosky, J., 1987, Geophysical Fluid Dynamics., 2nd edition,
Springer-Verlag
- Pedlosky, J., 1996, ocean circulation theory, Springer-Verlag,
Berlin-Heidelberg-New York.
- Pedlosky, J., 2003, waves in the ocean and atmosphere.,
Springer-Verlag, Berlin-Heidelberg-New York.
- Gill, A. E, 1982, Atmosphere-ocean dynamics, Academic Press,
London
Homework will be given throughout the course. The best 80% of the
homework will constitute 40% of the final grade. Each student will be
invited to present a brief informal description of some aspects of the
ocean circulation and its role in climate (20%), see details
here
for a list of possible
subjects. The times of the presentations are given
here. The final exam
will be a take home (40%).