METEO 520 Geophysical Fluid Dynamics

Geophysical Fluid Dynamics Instructor: Prof. Marcelo Chamecki Lectures: Monday, Wednesday, Friday 11:15AM-12:05PM in 101 Walker

Meteo 520 Geophysical Fluid Dynamics

General information

  • Instructor: Prof. Marcelo Chamecki
  • Office: 506 Walker
  • Phone: (814) 863-3920
  • Email:
  • Lectures: Monday, Wednesday, Friday 11:15AM-12:05PM in 101 Walker
  • Office hours: Wednesday 4:30-5:30 PM or by appointment

Course content

This is a course in the fundamentals of uid 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, some exact solutions, and rotating shallow water waves. 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.

Textbook and reading assignments

The textbook1 for this course will be Fluid Mechanics by P. K. Kundu, I. M. Cohen and D. R. Dowling. The book covers most of the topics that will be presented in the course with a good balance between physical interpretation and mathematical treatment. The reading assignments and part of the homework problems will be specied from the textbook. It is essential that all text assignments are carefully read. In addition, the assigned sections constitute a minimal portion of what should be read. Students should identify other sections and other reference books (some suggestions listed below) according to their own interests. 1Penn State honors and values the socioeconomic diversity of our students. If you require assistance with the costs of textbooks for this course, contact the Oce of Student and Family Services (120 Boucke Building, 863-4926, For additional need related to socioeconomic status please visit

Course evaluation

Students will be evaluated based on homework sets, two midterms and a final exam. Although homework sets only contribute 10% of the final grade, it is mandatory that you turn them in. I strongly recommend that you work the assigned problems on your own and ask ME questions if you get stuck. Homeworks will be distributed in class and/or uploaded to the PSU Angel website. I do not give full marks to homeworks handed after the due date. The exams are open notes and open book (you can only use your own notes and the textbook) and are designed to test your understanding of the fundamentals and whether you can apply the basic concepts to situations not covered in the homework or textbook. Final grade composition: 

  1. Problem sets 10%
  2. Midterm examinations 25% each
  3. Final examination 40%

Tentative schedule:

  • Midterm 1 - Tuesday October 2nd
  • Midterm 2 - Tuesday November 6th
  • Final - Sometime during the nals period

Except for illness, make-up exams will be conducted only for students who make arrangements with me prior to the scheduled exam time.

List of recommended references

This is a list of useful references for our course. I strongly recommend that you choose at least one or two of these books as additional sources of information to our textbook (in particular the classic book by Batchelor and the illuminating album of pictures by Van Dyke).

  1. Introductory books: 
    • Introduction to Fluid Mechanics by R. W. Fox, A. T. McDonald and P. J. Pritchard 
  2. More advanced books: 
    • An Introduction to Fluid Dynamics by G. K. Batchelor
    • Fluid Mechanics by L. D. Landau and E. M. Lifshitz 
  3. Atmospheric dynamics books:
    •  Geophysical Fluid Dynamics by B. Cushman-Roisin
    • Atmosphere-Ocean Dynamics by A. E. Gill
    • Geophysical Fluid Dynamics by J. Pedlosky
    • Atmospheric and Oceanic Fluid Dynamics by G. K. Vallis 
  4. Specialized books:
    • Vectors, Tensors and the Basic Equations of Fluid Mechanics by R. Aris
    • Vortex Dynamics by P. G. Saman 
  5. More \visual" material
  • An Album of Fluid Motion by M. Van Dyke
  • Multimedia Fluid Mechanics (DVD) by G. M. Homsy
  • A collection of classic videos (on-line and FREE):

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. See Earth and Mineral Sciences Academic Integrity Policy which this course adopts.

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 instructors 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 Universitys Code of Conduct, and/or liable under Federal and State laws. 


This course abides by the Penn State Class Attendance Policy 42-27 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, 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.

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.

Accommodations for students with disabilities

The Office of Disability Services requests and maintains disability-related documents; certies eligibility for services; determines academic adjustments, auxiliary aids, and/or services; and develops plans for the provision of academic adjustments, auxiliary aids, and/or services as mandated under Title II of the ADA Amendments Act (ADAAA) of 2008 and Section 504 of the Rehabilitation Act of 1973. A list of these services is provided at Weather delays Campus emergencies, including weather delays, are announced on Penn State News and communicated to cellphones, email, the Penn State Facebook page, and Twitter via PSUAlert

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 discussed in class. 

Tentative schedule

This is a tentative schedule, which will probably not be followed in detail. I am listing this information here so that you can read the corresponding material on the textbook ahead of time. Lectures marked with a * will likely need to be rescheduled.

Lecture Day Topic Textbook

  • 08/24 Introduction Chapter 1
  • 08/26 Math review Chapter 2
  • 08/28 Math review
  • 08/31 Math review
  • 09/02 Kinematics - Material derivative Chapter 3
  • 09/04 Kinematics - Decomposition of motion
  • 09/09 Kinematics - Decomposition of motion
  • 09/11 Kinematics - Streamlines
  • 09/14 Kinematics - Vortical ows
  • 09/16 Kinematics - Vortical ows
  • 09/18 Kinematics - Reynolds Transport Theorem
  • 09/21 Kinematics - Reynolds Transport Theorem
  • 09/23 Conservation laws - Mass Chapter 4
  • 09/25 Conservation laws - Momentum
  • 09/28 Conservation laws - Momentum
  • 09/30 Conservation laws - Navier-Stokes Equations
  • 10/02 Midterm 1
  • 10/05 Conservation laws - Navier-Stokes Equations
  • 10/07 Conservation laws - Integral balances
  • 10/09 Conservation laws - Rotating frame of reference
  • 10/12 Conservation laws - Energy
  • 10/14 Conservation laws - Bernoulli
  • 10/16 Conservation laws - Boussinesq Approximation
  • 10/19 Conservation laws - Boussinesq Approximation
  • 10/21 Conservation laws - Boundary conditions
  • 10/23 Vorticity dynamics - Kelvin's Theorem Chapter 5
  • 10/26 Vorticity dynamics - Kelvin's Theorem
  • 10/28 Vorticity dynamics - Vorticity equation
  • 10/30 Vorticity dynamics - Vorticity equation
  • 11/02 Vorticity dynamics - Vorticity equation
  • 11/04 Vorticity dynamics - Point vortices
  • 11/06 Midterm 2
  • *11/09 Similarity - Scaling analysis 1.11 and 4.11
  • *11/11 Similarity - Dimensional analysis
  • *11/13 Similarity - Dimensional analysis
  • 11/16 Some exact solutions - Laminar parallel ows Chapter 8
  • 11/18 Some exact solutions - Laminar parallel ows
  • 11/20 Some exact solutions - Creeping ows
  • 11/30 Applications in GFD { Flow around Planet Earth Chapter 13
  • 12/02 Applications in GFD { Geostrophic balance
  • 12/04 Applications in GFD
  • 12/07 Rotating shallow water waves Chapter 6
  • 12/09 Rotating shallow water waves Chapter 13
  • 12/11 Rotating shallow water waves

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