Geophysical Fluid Dynamics-1 Winter 2001 OC 512a/ ATM 509 SLN: 5814

lectures: MWF 9.30-10.20; OSB room 425

lab demo hour: F 10.30; OTB room 206 or OSB 107

P.B. Rhines rhines@ocean.washington.edu Ocean Sciences room 319 tel 3-0593

L. Thomas leif@ocean.washington.edu Ocean Sciences room 308 tel 3-0769

Web site: www.ocean.washington.edu/courses/oc512

OUTLINE (associated math in bold text)

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oceans and atmospheres: general description

buoyancy, pressure, stable stratification, mean vertical structure

rotation, geopotential, Coriolis force

scale analysis

geostrophic balance

equations of motion;

Cartesian

sphere

adiabatic; diabatic => basic thermodynamics

particle on an f-plane

long gravity waves with rotation method of characteristics

waves; Poincare, Kelvin

waves and circulations

hydrostatic balance forced/free solutions (homogeneous/particular)

geostrophic adjustment-I

geostrophic flow

Rossby deformation radius

energetics

rotational stiffness

Ekman layers – I boundary-layer (singular perturbation) theory

wind-driven channel flow

meridional circulation

continuously stratified fluids

geostrophic adjustment-II

thermal wind

Prandtl ratio, Burger number

potential/kinetic energy

velocity spirals

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

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

Rossby waves I: single-layer fluid

pv robustness, Ñ·J; 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:

QG flow over a mountain

potential vorticity production: Shaer, lab..

thermally forced vortex; convection -I

Rossby waves-II

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

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LABS (not necessarily in this order)

1. Pressure, buoyancy, eqn of state, heat content and flux; surface effects, evaporation, droplets; low-pressure fluids: boiling and freezing, clinking, latent heat transport in 2-chamber vessel.

2. 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

3. 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

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 b 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)

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).