Introduction to physical oceanography

EPS 131 (Fall 2005)

Instructor: Eli Tziperman,

TF: Laure Zanna,, 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

Textbooks Outline Detailed Syllabus Additional reading Requirements Links

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
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: Also interesting:


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.

Detailed syllabus

(Somewhat more detailed lecture notes, other images and supporting-material.)

  1. Outline and motivation. lecture1
  2. 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).
  3. 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 $R=U/(fL)$, and Ekman number $E=\nu/(fL^2)$; 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.
  4. 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.
  5. Inertial oscillations (Kn p 108-109), equations and circular trajectories of fluid parcels.
  6. 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);
  7. 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);
  8. Ekman pumping (Kn p 125-128); Ekman spiral, (Kn p 124); curl tau from observations; North Atlantic subtropical and sub polar gyres;
  9. Mid term review: which terms in the Navier Stokes equations are responsible for: inertial motions ($e1{\sim}e2$), damped inertial motions ($e1{\sim}e2+e6$), geostrophy ($e2{\sim}e3$), Ekman layers/ drift ($e2{\sim}e5$), buoyancy oscillations ($g1{\sim}g3$), hydrostatic balance ($g2{\sim}g3$). In temperature equation: abyssal recipes and exponential temperature profile ($b1{\sim}b2$); vertical velocity being so small ( $a1{\approx}a2{\gg}a3$).
  10. 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.
  11. 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).
  12. 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.
  13. 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.
  14. Practicalities: using Matlab, solving a simple advection-diffusion numerically: leap frog, center space differencing, Robert Filter.
  15. El Nino:
  16. 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

Additional reading:

Beginning texts: Intermediate texts: Advanced texts:


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%).