## Introduction to Geophysical Fluid Dynamics Fall 2009

• AMATH & ATM S 505A, OCEAN 511A (4 Credits)
• Meetings: MWF 11:30-12:20, LOW 101, plus 4th hour: 10:30-11:20 OR 12:30-1:20 Fridays (Locations TBD and will vary week-to-week)
• Instructor: Parker MacCready, parker@ocean.washington.edu, (68)5-9588, OCN 311, office hours by appointment
• TA: Cathy Yang, ykc1208@u.washington.edu, (61)6-9682, office hours: Wednesdays 10:30-11:20 am and Fridays 2:30-3:20 pm at OSB 245
• Textbook (required): Fluid Mechanics by Kundu and Cohen (preferably 4th ed.).
Copies are available at the bookstore in the ATM SCI section

DESCRIPTION: This class is for first year grad students in Atmospheric Science, Oceanography, Civil, Environmental, and Mechanical Engineering, and related disciplines. It is meant to be a rigorous introduction to basic aspects of fluid flow, from its molecular origins (what is pressure? what is viscosity?) to simple large scale behavior (why does atmospheric temperature decrease with height?). And of course we cover the fun things - like how vortices interact and why waves move the way they do. We develop and apply the important tools of fluid understanding: conservation of mass, momentum, energy, and vorticity. And we learn how to apply different reference frames (a point in space, a point following the fluid, a surface, a volume) to see problems in different ways.

CATALOG DESCRIPTION: Eulerian equations for mass, motion; Navier-Stokes equation for viscous fluids, Cartesian tensors, stress, strain relations; Kelvin's theorem, vortex dynamics; potential flows, flows with high, low Reynolds numbers; boundary layers, introduction to singular perturbation techniques; water waves; linear instability theory. Prerequisite: AMATH 403 or permission of instructor.

• Homework: 60% (OK to work with others, but write it out yourself)
• Midterm 15% (take home, open book, open notes)
• Final 25% (take home, open book, open notes)

SYLLABUS (KC=Kundu & Cohen Reading, PS=Problem Set Assigned: due 1-week later at start of class)

 I. Fundamental Fluid Concepts and Conservation Equations W 9/30 I.1 Organization, the scope of fluid mechanics and this class, the continuum hypothesis KC 1.1-5 F 10/2 I.2 Fluid parcel, Density, Pressure and its molecular origins, the net force on a fluid parcel due to pressure KC 1.7, 2.1-6 M 10/5 I.3 The pressure gradient, hydrostatic balance PS 1 KC 2.7-10 W 10/7 I.4 Velocity, Lagrangian vs. Eulerian point of view, the material derivative KC 3.1-7 F 10/9 I.5 Conservation of mass, incompressible flow Lab: Buoyancy and the Spar Buoy High-Bay area of the Ocean Sciences Building 1st floor (OCN) pdf map KC 2.13, 3.13, 4.1-3, 4.18 M 10/12 I.6 Gauss Divergence Theorem, Buoyancy, Momentum conservation (inviscid) PS 2 PS 1 Solutions KC 4.4-8 II. Scaling, the Shallow Water Equations, Waves, and the Bernoulli Function W 10/14 II.1 Scaling: the Boussinesq and Hydrostatic Approximations Holton 2.4.3, KC 4.18 F 10/16 II.2 Shallow Water (SW) Equations Lab: Wave Tank MacCready Lab OCN 147 (Ocean Sciences Building) map M 10/19 II.3 Shallow water waves I KC 7.1-3 W 10/21 II.4 Shallow water waves II F 10/23 II.5 Bernoulli function KC 4.16-17 Lab: Flume with flow over a bump OTB 206 (Ocean Teaching Building) map III. Viscosity and Energy M 10/26 III.1 Viscosity, molecular origins, effects on momentum, Reynolds number, Couette flow KC 9.1-6 W 10/28 III.2 Viscosity continued... PS 3 Solutions F 10/30 Energy: derivation of the KE conservation equation Control Volume Analysis, Momentum Integral KC 4.8 again, KC 4.13 Extra Hour Rooms: 10:30 in LOW 113, 12:30 LOW 105 M 11/2 MOVIE: Pressure Fields & Fluid Acceleration W 11/4 MOVIE: Waves in Fluids F 11/6 III.5 KE & PE per unit volume Midterm Solutions M 11/9 III.6 KE & PE for Shallow Water Waves PS 4 W 11/11 Veteran's Day Holiday IV. Vorticity F 11/13 IV.1-2 Vorticity 1: Definitions and Examples Lab: Pool-Vortex Rings High-Bay area of the Ocean Sciences Building 1st floor (OCN) map KC 5.1-4 M 11/16 Vorticity 2: Kelvin Circulation Theorem & Helmholtz Vortex Theorems PS 4 Solutions KC 5.5-7 W 11/18 IV.3 Vorticity 3: Vorticity Equation PS 5 KC 5.8-9 V. Potential Flow F 11/20 V.1 Potential Flow 1: Definitions Open question session KC 6.1-7 M 11/23 V.2 Potential Flow 2: Solutions KC 6.8-9 W 11/25 V.3 Potential Flow 3: Drag on a Cylinder PS 5 Solutions F 11/27 Day-After-Thanksgiving Holiday VI. Deep-water Waves, 2-layer Stratification, K-H Instability M 11/30 VI.1-2 Deep water waves (nonhydrostatic) PS 6 KC 7.4-6 W 12/2 Dispersion, group velocity vs. phase speed KC 7.7-10 F 12/4 VI.3-5 Instability of fluid flows Lab: 2-Layer Waves MacCready Lab OCN 147 (Ocean Sciences Building) map KC 12.1-6 M 12/7 Kelvin-Helmholtz Instability W 12/9 K-H Instability, continued VII. Compressibility F 12/11 VII.1 Effects of compressibility, Sound Waves KC 1.8-10 & 16.1-2 Open question sessions: 406 Atmospheric Sciences Building map M 12/14 Final exam due 11:30 AM in box outside OSB 313 Final Exam Answers & Extra on Problem 3

RECOMMENDED BOOKS

• Acheson, D. J. (1990) Elementary Fluid Dynamics. Oxford University Press, 397 pp. Simple and elegant. More emphasis on aeronautics.
• Batchelor, G. K. (1967) An Introduction to Fluid Dynamics. Cambridge University Press, 615 pp. The classic text, authoritative, somewhat dated and difficult to get through early in your education. Definitely worth consulting when you need a deeper understanding.
• Gill, A. E. (1982) Atmosphere-Ocean Dynamics. Academic Press, 662 pp. A wonderfully-broad introduction to the topic of geophysical flows, often with very insightful derivations and explanations. Often used as the primary reference text for GFD I.
• Holton, J. (1979) An Introduction to Dynamic Meteorology. Very clear explanations of fluid mechanics and basic GFD, especially for atmospheric flow.
• Tritton, D. J. (1977) Physical Fluid Dynamics. Van Nostrand Reinhold, 362 pp. A more casual, and intuitively-pleasing treatment of incompressible flow at small to medium scales. No free surfaces, but lots of discussion of how real flows are affected by turbulence.
• Muller, P. (2006) The Equations of Oceanic Motion. Cambridge University Press, 291 pp. This is probably not suitable for beginners, but if eventually you want a really rigorous derivation of the equations we use, this is the best reference I have found.
• Prandtl, L. and O. G. Tietjens (1934) Fundamentals of Hydro- and Aeromechanics. Dover Publications, 270 pp. A beautifully-written introduction by one of the great modern masters. Here you will see many of the derivations that have ended up in Kundu and Cohen.

FLUID MECHANICS MOVIES

The classic series of Fluid Mechanics Movies, some of which we show, are available on the web
http://web.mit.edu/fluids/www/Shapiro/ncfmf.html