Introduction to physical oceanography

EPS 131 (Spring 2004)

Instructors: Eli Tziperman, Ian Eisenman

[This course was previously taught by Prof Allan Robinson]

Day, time & location: Tue, Thu, 10-11:30, Cruft 319.

Homework: 01, 02, 03, 04, 05, 06, 07, 08 (Due Fri Apr 30, and no later...),

Ian's homework solutions: 01, 02, 03, 04, 05, 06, 07, 08,

Matlab programs: pipe_1d_tracer.m,

Ian's Matlab seminar files: here or here: Advertisement examples: ripples.m, levitus94_temp_profile.m, standard_map.m; Matlab basics worksheet: worksheet.pdf; Finite difference example: finite_diff_ex.m; Leapfrog method handout: leapfrog.pdf; Diffusion and advection of a tracer in a narrow looped pipe: pipe_1d_tracer.m;

Gravity waves, the movie: Chelsey, Ben, Philip movie 1, Philip movie 2, Philip pic 1, Philip pic 2, director: Sarah, main actor: Philip, Kurt, Ian(!): an animated full feature, watch this one to see what you are supposed to notice in the other movies,

Student presentations.

Textbooks:

• (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.
• (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.

Outline

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

1. Outline and motivation.
2. Basics: Continuum hypothesis, pressure, hydrostatics (Ku 1.4-1.5, p 4; 1.7 p 9-11). Kinematics: Eulerian vs Lagrangian, material derivative, stream line (Ku 3.1-3.4 p 50-56), stream function (Ku 3.13, p 69-70). Continuity equation (mass conservation, Kn, Box 4.1 p 69), temperature equation (conservation of heat, Kn, Box 4.2 p 74-75). Equation of state. Ocean: the overturning ocean circulation and the vertical temperature profile in the ocean, solar radiation and air-sea heat fluxes (Ku p 39-61).
3. Momentum equations: acceleration, pressure force, gravity, friction, Coriolis force (Kn, chapter 5, p 80-107; for Coriolis, a better source is Ku section 4.12 p 99-101). Atmosphere/ ocean: geostrophy (Kn p 110), thermal wind, problem of the ``level of no motion'', weather systems and pressure highs and lows/ ocean gyres and ocean surface height.
4. Density, potential temperature, potential density, sigma theta, sigma-4 , stability, Brunt Vaisala frequency (OU p 230-232; Kn p 29-34, 38) and buoyancy oscillations(*), T-S diagrams and mixing of water masses (OU p 225-229), T-S distribution (Kn p 163-183).
5. Rossby number, inertial oscillations (Kn p 108-109), equations and circular trajectories of fluid parcels(*).
6. Friction: molecular, turbulent, horizontal vs vertical friction in the ocean (Kn p 98-101); bottom friction parameterization (Kn p 97); scale selective vs non scale selective friction; inertial motions with friction (Kn p 120);
7. Combined effects of friction, wind and rotation: 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, fisheries and El Nino (OU p 133-137, 153-155);
8. 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.
9. Ekman pumping (Kn p 128); Ekman spiral, (Kn p 124); curl tau from observations; North Atlantic subtropical and sub polar gyres; beta v=f dw/dz (Kn, p XX); Sverdrup balance (beta v = curl tau).
10. f=f(y), beta=df/dy, 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. Idealized ocean basic and calculating v from the Sverdrup balance and then u. 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 (Kn 192-198): vector vorticity, irrotational flow (vorticity=0, velocity=gradient of potential); Bernoulli function (simple linearized version) and boundary conditions on velocity potential; wave solution in 2d (x,z) and dispersion relation; limits of shallow and deep ocean; particle trajectories; phase and group velocities; dimensional arguments for deep and shallow gravity wave dispersion relations. Tsunamis as shallow waves, waves refraction when approaching a curved beach. Other waves mentioned briefly: internal waves, Poincare waves, coastal and equatorial Kelvin waves, Rossby waves and a heuristic explanation of westward propagation.
13. Practicalities: using Matlab, solving a simple advection-diffusion numerically: leap frog, center space differencing, Robert Filter.
14. Ian's El Nino lecture.
15. 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 in each of these files): 1, 2, 3

Additional reading:

• 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,

• 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,

• 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

Requirements

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 final exam will be a take home (40%).

Links

• First lecture.
• Ian's El Nino lecture.
• Coriolis force movies: here and here; and here is another nice Coriolis force home page with demos and animations