Instructor: Peter Bannon Lectures: Tues. and Thurs. at 10:35-11:50 a.m. in 101 Walker Building

This course presents 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 geophysical applications of them. Together, Meteo 520 and Meteo 521 (Dynamic Meteorology) make up the core dynamics curriculum for graduate students of meteorology.

Course Structure: 

Examinations: Two midterms and a final exam are planned. The midterms are scheduled for September 29th and November 3rd. Each mid-term will contribute 25% to your final grade, the final 30%.  

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

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

Lectures: Tues. and Thurs. at 10:35-11:50 a.m. in 101 Walker Building 

Peter R. Bannon, 521 Walker Building, 814-863-1309, Office hours: 12:10-1:30 p.m. Tues. and Thurs., by appointment, or whenever my door is open


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

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. 


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

  2. 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)

  3. 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, streamfunction

  4. 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

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

  6. Exact steady-state solutions
    Stokes flow around a sphere
    Geostrophic flow
    Ekman flow

  7. Dynamic similarity
    Dimensional analysis
    Buckingham Pi theorem

  8. 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.


  • *Acheson, D. J., 1990: Elementary Fluid Dynamics. Oxford, 397 pp. TA357.A276 1990 ENG
  • 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, 2016: Fluid Mechanics. Sixth Edition.  Academic Press, 921 pp.  QA901.K86 2016 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 

Prerequisites: Students who do not meet these prerequisites may be disenrolled according to Administrative Policy C-5. if they do not have the proper prerequisite override. Students who re-enroll in the course after being dis-enrolled according to this policy are in violation of Item 15 on the Student Code of Conduct:

Assistance with Textbooks: Penn State honors and values the socioeconomic diversity of our students. If you require assistance with the costs of textbooks for this course, contact the Office of Student and Family Services (120 Boucke Building, 863-4926, For additional need related to socioeconomic status please visit

Academic Integrity 

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:, which this course adopts. To learn more, see Penn State's "Plagiarism Tutorial for Students."

Course Copyright 

All course materials students receive or to which students have online access are protected by copyright laws. Students may use course materials and make copies for their own use as needed, but unauthorized distribution and/or uploading of materials without the instructor’s express permission is strictly prohibited. University Policy AD 40, the University Policy Recording of Classroom Activities and Note Taking Services addresses this issue. Students who engage in the unauthorized distribution of copyrighted materials may be held in violation of the University’s Code of Conduct, and/or liable under Federal and State laws.

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) website provides contact information for every Penn State campus: ( For further information, please visit the Office for Disability Services website ( 

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 based on the documentation guidelines ( If the documentation supports your request for reasonable accommodations, your campus’s disability services office will provide you with an accommodation letter. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations.


This course abides by the Penn State Attendance Policy E-11:, and Conflict Exam Policy 44-35: Please also see Illness Verification Policy:, and Religious Observance Policy: 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, military service, family emergencies, regularly scheduled university-approved curricular or extracurricular activities, and post-graduate, career-related interviews when there is no opportunity for students to re-schedule these opportunities (such as employment and graduate school final interviews). 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: Whenever possible, students participating in University-approved activities should submit to the instructor a Class Absence Form available from the Registrar's Office:, at least one week prior to the activity.

Weather Delays

Campus emergencies, including weather delays, are announced on Penn State News and communicated to cell phones, email, the Penn State Facebook page, and Twitter via PSUAlert (Sign up at:

Syllabus and Paper Acknowledgement Forms
All students must sign and return the Syllabus Acknowledgement Form during the first week of the semester.

Penn State E-mail Accounts

All official communications from Penn State are sent to students' Penn State e-mail accounts. Be sure to check your Penn State account regularly, or forward your Penn State e-mail to your preferred e-mail account, so you don't miss any important information. 

Deferred Grades

If you are prevented from completing this course within the prescribed amount of time, it is possible to have the grade deferred with the concurrence of the instructor. To seek a deferred grade, you must submit a written request (by e-mail or U.S. post) to your instructor describing the reason(s) for the request. It is up to your instructor to determine whether or not you will be permitted to receive a deferred grade. If, for any reason, the course work for the deferred grade is not complete by the assigned time, a grade of "F" will be automatically entered on your transcript. 

Military Personnel

Veterans and currently serving military personnel and/or spouses with unique circumstances (e.g., upcoming deployments, drill/duty requirements, disabilities, VA appointments, etc.) are welcome and encouraged to communicate these, in advance if possible, to the instructor in the case that special arrangements need to be made. 

Technical Requirements

For this course, we recommend the minimum technical requirements outlined on the Dutton Institute Technical Requirements page (, including the requirements listed for same-time, synchronous communications. If you need technical assistance at any point during the course, please contact the ITS Help Desk (


The term "Netiquette" refers to the etiquette guidelines for electronic communications, such as e-mail and bulletin board postings. Netiquette covers not only rules to maintain civility in discussions, but also special guidelines unique to the electronic nature of forum messages. Please review some general Netiquette guidelines that should be followed when communicating in this course. 

Disclaimer Statement

Please note that the specifics of this Course Syllabus can be changed at any time, and you will be responsible for abiding by any such changes. Changes will be posted.