Geophysical Fluid Dynamics-1 Winter 2004 OC 512/ ATM 509
lectures: MWF 10.30-11.20; ATG 310
lab demo hour: Th 2.30; OSB room 107 (or sometimes OTB 206)
P.B. Rhines rhines@ocean.washington.edu Ocean Sciences room 319 tel 543-0593
D. Kirshbaum dank@atmos.washington.edu Atmos Sci room 620 tel 685-9305
E. Lindahl lindahl@ocean.washington.edu Ocean Sciences room 107 (GFD Lab) tel 543-2515 Web site: www.ocean.washington.edu/courses/oc512/gfd1.html


OUTLINE (associated math in brackets, will be introduced briefly)
==========================
oceans and atmospheres: general description
modern observations
general circulation: thin layered structure of ocean and atmosphere; dominant horizontal velocity and weaker yet important meridional overturning circulation: convection at all scales; pv work
energy as a unifying principle
solar radiation: black body radiation, ultraviolet, visible, infrared; the greenhouse ‘blanket’
buoyancy, pressure, stable stratification, mean vertical structure
Earth’s rotation
scale analysis
geostrophic balance observed
equations of motion;
balance and evolution
motionless fluids: geopotential, hydrostatic balance
F=ma for a fluid vector calculus identities
Cartesian trigonometry
sphere
equation of state: adiabatic; diabatic => basic thermodynamics
particle on an f-plane

long gravity waves with rotation {method of characteristics hyperbolic p.d.e.}
waves; Poincare, Kelvin
waves and circulations
hydrostatic balance {separation of variables
forced/free solutions (homogeneous/particular)}
{scale analysis and dimensional analysis}
geostrophic adjustment-I
geostrophic balanced flow
Rossby deformation radius
energetics
rotational stiffness

continuously stratified fluids
geostrophic adjustment-II
thermal wind
Prandtl ratio, Burger number
potential/kinetic energy
velocity spirals

Ekman layers – I the diffusion equation (parabolic p.d.e.)}
wind-driven channel flow {boundary-layer theory}
vorticity and potential vorticity (PV-) dyamics
Kelvin’s and Bjerknes circulation theorems
em analogies
spin and angular mom
vorticity and pv inversions
vortex stretching and tipping
Ekman layers – II: spin-up
frictionally driven meridional circulation
Rossby waves I: single-layer fluid
pv robustness, ; conservation, sources and sinks
energy dissipation; enstrophy dissipation
transport of scalar and vector quantities by waves and eddies
geostrophic scaling: {regular pert theory => perturbed eigenvalue}
synoptic QG (quasi-geostrophic) equation: {LaPlace/Poisson equation}

QG flow over a mountain {elliptic pde}
potential vorticity production
thermally forced vortex; convection -I
Rossby waves-II

internal waves
Boussinesq, atmos model with compressibility
{group velocity ‘wave mathematics multi-scale analysis (two-timing); Fourier analysis, eigenmodes, eigenvalues}
mountain waves
modes and turning points with non-uniform stratification

Some extra topics, if time permits:
baroclinic energy conversion
meridional circulations
convection –II: convective heat transport
in boundary layers
at global scale {chaos: low-order, nl systems}
intense eddies, vortices
vortex pair
merger, 2DT
vortex stretching limited
thermally forced vortex
hydraulics
downslope flow, solitons, undular bore
advection/diffusion {similarity variables}
==========================

LABS (not necessarily in this order)

1. Pressure, buoyancy, eqn of state, heat content and flux; U-tube oscillator, surface effects, evaporation, droplets; low-pressure fluids: boiling and freezing, clinking, latent heat transport in 2-chamber vessel. (order changed)
2. Coriolis effects: equilibrium geoid; stiff columns; Taylor Proudman, Coriolis force on a jet; inertial waves; Kelvin waves/gravity current; tornado vortex, rotating flow over mountain
3. Waves-I Overhead projector ripples, mean flow. U-tube; one- and two-layer gravity waves, particle paths; wave packet, group velocity; solitons, gravity current, mean flows; piano and surface tension modes
4. Geostrophic flow, geostrophic adjustment in a channel (Gill), geostrophic adjustment of cylindrical blob; thermal wind shear (narrow gap annulus exp); river outflow plume.
5. Ekman layers and spin-up. Boundary layers, Ekman veering; Wedding cake (vertical shear layers); sink flow (purple tornado); spin-up time (energetic argument); effects of stratification; coastal upwelling, fronts
6. Waves –II continuous stratification, int. grav waves, mountain waves hydraulics, estuary model, kitchen sink bore, 8’ flume undular bores, numerical model
7. Stirring and mixing and their dynamical products. Basic diffusion of heat and dye in a column; heat and tracer flux enhanced by fluid strain (onion slice with fluorescein); stirring and mixing; convection and boundary layers; turbulent jet entrainment; estuary; double diffusion and layering.
8. Global heat engine, meridional circulation, heat flux and baroclinic instability. rotating annulus exper: narrow (stable zonal flow)/med (wave regime; jets and eddies) /wide gap (geost. turbulence) Thermal wind measured; non-rotating slot
9. Rossby waves and potential vorticity. Polar ? plane; induced zonal jets, polar vortex; oscillatory Charney-deVore (Boris ridge-ed bowl); barotropic instability, vortex interactions.

TEXT: Gill, A.E., Atmosphere-Ocean Dynamics, Academic Press

OTHER REFERENCES

Pedlosky, J., Geophysical Fluid Dynamics, Springer Verlag
(complements Gill, emphasizing QG dynamics, Rossby waves, baroclinic instability, non-dimensional scaling)
James, I.N. Introduction to Circulating Atmospheres, Oxford Univ. Press (good basic discussion of modern atmospheric circulation dynamics)
many good review papers on GFD of A and O can be found in Annual Reviews of Fluid Mechanics, a yearly hard-bound collection.
Meteorology at the Millenium, R.B.Pearce Ed., Academic Press (a recent collection of review papers on atmospheric circulation some with a GFD emphasis).
Large-Scale Dynamical Processes in the Atmosphere. Academic Press, Hoskins and Pearce Eds. (an old (1983) yet still excellent set of review papers on basic circulation)
Evolution of Physical Oceanography MIT Press,Warren and Wunsch Eds. (also old, ca. 1981, yet excellent review papers on physical oceanography, general circulation).
Acheson, D. Elementary Fluid Mechanics, Oxford Univ. Press (excellent, terse introduction to classical fluid mechanics)

Lighthill, M.J., An informal introduction to theoretical fluid mechanics. Oxford Univ. Press (especially expert discussion by a master of vorticity, and of sound propagation)
Lighthill, M.J., Waves in Fluids. Cambridge Univ. Press (basic wave mathematics, of non-dispersive and dispersive wave types; ray-tracing; internal and Rossby waves).
Whitham, G.B. Linear and Nonlinear Waves. Wiley and Sons (a remarkable presentation of non-dispersive and dispersive waves from a fundamental mathematical point of view).
Salmon, R., Lectures on Geophysical Fluid Dynamics, Oxford Univ. Press (another remarkable, recent text treating mostly large-scale QG oceanic GFD but with

fundamental ideas about fluid dynamics based on Hamilton’s principle)
James, I., Introduction to Circulating Atmospheres (readable discussion of basic GFD of the large-scale atmosphere)
Batchelor,G.K., An Introduction to Fluid Dynamics, Cambridge Univ. Press (impeccable reference on basic incompressible fluids, vorticity, strain, boundary layers)
Kundu,P. Fluid Dynamics, Academic Press (includes sections on elementary GFD)
Tritton, D., Physical Fluid Dynamics (basic fluids from a GFD point of view).
Van Dyke,M. An Album of Fluid Motion, Parabolic Press (amazing photographs of basic fluid dynamics).

Landau and Lifshitz, Fluid Mechanics, Addison-Wesley (an early treatment of fluid dynamics by two great physicists).