# METEO 520 Bannon FA14

### GEOPHYSICAL FLUID DYNAMICS

#### Course Structure

Examinations:

Two midterms and a final exam are planned. The midterms are scheduled for October 3rd(or 6th) and November 14th. Each mid-term will contribute 25% to your final grade, the final 30%.

Problem Sets: Frequent problem sets (due every Wednesday) will be given. The problem sets will count towards 15% of your grade.

Textbooks: Fluid Mechanics by Kundu, Cohen, and Dowling.

Lectures: Mon., Wed., and Fri. at 11:15-12:05 p.m. in 218A Hosler

#### Lecturer:

Peter R. Bannon

521 Walker Building

bannon@ems.psu.edu

863-1309

Office hours: 12:30-1:30 p.m. Mon., Wed., and Fri.,by appointment, or whenever my door is open

Policies:

- Student participation in class is essential. 5% of your grade will be assigned based on your individual level of participation.
- Total scores are curved to determine the course grade.
- 20% penalty for homework turned in after 3:00 p.m. on the due date.
- No homework will be accepted after the answers are posted or discussed in class.
- Make-up exams by prior arrangement only.
- No make-up final except for a direct conflict.
- This course adopts the academic integrity policy of the EMS College that is described at

*http://www.ems.psu.edu/current_undergrad_students/academics/integrity_policy*

Briefly, students are expected to do their own problem sets and to work the exams on their own. Class members may work on the problem sets in groups, but then must write up their answers separately. Students may not copy problem or exam answers from another person's paper and present them as their own.

#### GEOPHYSICAL FLUID DYNAMICS

- Introduction

- Definition of a fluid: gases and liquids
- Continuum hypothesis: the fluid parcel
- Mathematical review: vector and tensor analysis

- Forces acting on a fluid

- Body forces: gravity, geopotential
- Surface stresses
- Stress tensor in a fluid at rest: pressure
- Hydrostatic balance
- Buoyancy force
- Surface tension (optional)

- Kinematics

- Lagrangian and Eulerian descriptions of the flow
- Acceleration: local and convective rates of change
- Analysis of motion in the vicinity of a point: divergence, deformation, and vorticity
- Strain rate tensor
- Vorticity kinematics
- Streamlines, trajectories, stream function

- Conservation laws

- Conservation of mass
- Newton's second law
- Stress tensor in a fluid in motion
- Effects of rotation: Coriolis and centrifugal forces
- First law of thermodynamics
- Equation of state
- Energetics: kinetic, potential, and mechanical energy equations
- Bernoulli equations

- Vorticity dynamics

- Vorticity equation
- Circulation theorems
- Helmholtz theorems: interaction of vortices
- Ertel's theorem and potential vorticity

- Exact steady-state solutions

- Stokes flow around a sphere
- Geostrophic flow
- Ekman flow

- Dynamic similarity

- Dimensional analysis
- Buckingham Pi theorem

- Rotating shallow water wave dynamics

- Dispersion relation
- Wave structure
- Group velocity and energetics
- Geostrophic adjustment

#### Course Outline:

Please note that this outline serves only as a general guide to the course. The actual topics covered may vary at the discretion of the instructor.

#### Bibliography

- *Acheson, D. J., 1990: Elementary Fluid Dynamics. Oxford, 397 pp. EMS
- Aris, R., 1962: Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Prentice-Hall, 286 pp.
- *Batchelor, G. K., 1967: An Introduction to Fluid Dynamics. Cambridge, 615 pp. QA911.B33
- Brown, R. A., 1991: Fluid Mechanics of the Atmosphere. Academic Press, 489 pp.
- Chandrasekhar, S., 1961: Hydrodynamic and Hydromagnetic Stability. Dover, 652 pp.
- Cushman-Roisin, B., 1994: Introduction to Geophysical Fluid Dynamics. Prentice Hall, 320 pp.
- Drazin, P. G., and W. H. Reid, 1981: Hydrodynamic Stability. Cambridge, 527 pp.
- Dutton, J. A., 1995: Dynamics of Atmospheric Motion (formerly The Ceaseless Wind.) Dover, 617 pp. QC880.4.A8D88 1995
- Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 688 pp. GC190.G54 1982
- Greenspan, H. P., 1969: The Theory of Rotating Fluids. Cambridge, 328 pp.
- Hess, S. L., 1959: Introduction to Theoretical Meteorology. Holt, Rinehart and Winston, 362 pp.
- Holton, J. R. and G. K. Hakim, 2013: An Introduction to Dynamic Meteorology. Fifth Edition. Academic Press, 507 pp. QC880.H65 2013
- *Kundu, P. K., I. M. Cohen, and D. R. Dowling, 2012: Fluid Mechanics. Fifth Edition. Academic Press, 638 pp. QA901.K86 2012 EMS
- Lamb, H., 1932: Hydrodynamics. Sixth Edition, Dover, 738 pp. QA911.L2 1932
- Landau, L. D., and E. M. Lifshitz, 1987: Fluid Mechanics. Second Edition. Oxford, 539 pp.
- Lighthill, J., 1978: Waves in Fluids. Cambridge, 504 pp.
- *National Committee for Fluid Mechanics Films, 1972: Illustrated Experiments in Fluid Mechanics. M.I.T. Press, 251 pp. QC145.2.N37 EMS
- Pedlosky, J., 1986: Geophysical Fluid Dynamics. Second Edition. Springer-Verlag, 710 pp.
- Prandtl, L., and O. G. Tietjens, 1934: Fundamentals of Hydro- and Aerodynamics. Dover, 270 pp.
- Prandtl, L., and O. G. Tietjens, 1934: Applied Hydro- and Aerodynamics. Dover, 306 pp.
- Saffman, P. G., 1993: Vortex Dynamics. Cambridge, 322 pp.
- *Tritton, D. J., 1988: Physical Fluid Dynamics. Second Edition. Oxford, 519 pp. QC151.T74 1988 EMS
- Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge, 367 pp.
- Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge, 745 pp.
- *Van Dyke, M., 1982: An Album of Fluid Motion. Parabolic Press, 176 pp. TA357.V35 EMS

**(* on reserve)**

#### EMS Required Syllabus Topics

#### Brief course description from the University Bulletin:

METEO 520 Geophysical Fluid Dynamics (3) Fundamentals of fluid dynamics with an emphasis on basic concepts that are important for atmospheric and oceanic flows.

METEO 520 Geophysical Fluid Dynamics (3)

This is a course in the fundamentals of fluid dynamics with an emphasis on basic concepts that are important for geophysical flows, such as those in the atmosphere and ocean. Topics include kinematics, conservation laws, vorticity dynamics, dynamic similarity, laminar flows, and an introduction to waves and instability. Students should leave this course with a solid foundation in fluid dynamics, possessing a conceptual and mathematically rigorous understanding of the fundamental conservation laws for fluids and some basic applications of them. Together, METEO 520 and METEO 521 (Dynamic Meteorology) make up the core dynamics curriculum for graduate students of meteorology.

General Education: None Diversity: None Bachelor of Arts: None

Prerequisite: Vector calculus, differential equations

Note: Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

#### Course policies

This course abides by the Penn State Class Attendance Policy 42-27: *http://senate.psu.edu/policies/42-00.html#42-27*, Attendance Policy E-11: *http://www.psu.edu/oue/aappm/E-11.html*, and Conflict Exam Policy 44-35: *http://www.psu.edu/ufs/policies/44-00.html#44-35*. Please also see Illness Verification Policy: *http://studentaffairs.psu.edu/health/welcome/illnessVerification/*, and Religious Observance Policy: *http://www.psu.edu/oue/aappm/R-4.html*. Students who miss class for legitimate reasons will be given a reasonable opportunity to make up missed work, including exams and quizzes. Students are not required to secure the signature of medical personnel in the case of illness or injury and should use their best judgment on whether they are well enough to attend class or not; the University Health Center will not provide medical verification for minor illnesses or injuries. Other legitimate reasons for missing class include religious observance, family emergencies, and regularly scheduled university-approved curricular or extracurricular activities. Students who encounter serious family, health, or personal situations that result in extended absences should contact the Office of Student and Family Services for help: *http://studentaffairs.psu.edu/familyservices/*.

Whenever possible, students participating in University-approved activities should submit to the instructor a Class Absence Form available from the Registrar's Office: *http://www.registrar.psu.edu/student_forms/*, at least one week prior to the activity.

#### Academic integrity statement

Students in this class are expected to write up their problem sets individually, to work the exams on their own, and to write their papers in their own words using proper citations. Class members may work on the problem sets in groups, but then each student must write up the answers separately. Students are not to copy problem or exam answers from another person's paper and present them as their own; students may not plagiarize text from papers or websites written by others. Students who present other people's work as their own will receive at least a 0 on the assignment and may well receive an F or XF in the course. Please see: Earth and Mineral Sciences Academic Integrity Policy: *http://www.ems.psu.edu/current_undergrad_students/academics/integrity_policy*, which this course adopts.

#### Accommodations for students with disabilities

Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an office for students with disabilities. The Office for Disability Services (ODS) Web site provides contact information for every Penn State campus: *http://equity.psu.edu/ods/dcl*. For further information, please visit the Office for Disability Services Web site: *http://equity.psu.edu/ods*.

In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation: *http://equity.psu.edu/ods/guidelines*. If the documentation supports your request for reasonable accommodations, your campus’s disability services office will provide you with an accommodation letter.

#### Other statements as applicable

Residence Instruction: Campus emergencies, including weather delays, are announced on Penn State News: *http:/news.psu.edu/ *and communicated to cellphones, email, the Penn State Facebook page, and Twitter via PSUAlert (Sign up at: https://psualert.psu.edu/psualert/).