Instructor: Professor David Stensrud, 504 Walker,

Lectures: Tuesday and Thursday at 10:35-11:50 am, 214 Hammond

Office hours: Mondays 11:00 am -12:00 noon

Wednesdays 1:00 – 2:00 pm

Fridays 10:00 – 11:00 am 

Scope: 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. 

Homework: Problem sets will be assigned roughly every other week. You are expected to work independently to solve the problems though discussions among classmates are allowed and encouraged. Plagiarism will not be tolerated. Late homework will not be accepted. 

Readings:  Readings from both the book and from papers will be assigned routinely throughout the semester.  You are expected to read the materials and understand their content.

Grading: Office Hour Visit (5%), Homework (45%), two evening exams (15% each), and a final exam (20%). 

Textbook: Fluid Mechanics, Sixth Edition by Kundu, Cohen, and Dowling.  

Reserve materials:  The EMS Library has on reserve Fluid Mechanics by Kundu et al. and An Introduction to Fluid Dynamics by G. K. Batchelor.  You can find the 4th edition of the Fluid Mechanics book as an e-book online with Penn State libraries.             

Tentative Schedule:  Below is the tentative schedule for the course, along with where in the textbook the materials and concepts are discussed.  The actual pace of lectures will vary, so the schedule likely will not be followed exactly, although the order of the topics is about right.  

Lecture / Day / Topic / Textbook

  1. 8/21 Introduction Chapter 1
  2. 8/23 Math Review – Tensors Chapter 2
  3. 8/28 Math Review – Tensors Chapter 2
  4. 8/30 Theories of Gauss and Stokes Chapter 2
  5. 9/4 Kinematics of Fluid Motion Chapter 3
  6. 9/6 Decomposition of Fluid Motion Chapter 3
    Warren Washington Symposium
  7. 9/11 Strain and Rotation Chapter 3
  8. 9/13 Strain and Rotation Chapter 3
  9. 9/18 Streamlines, etc. Chapter 3
  10. 9/20 Kinematics of Vortex Flows Chapter 3
  11. 9/25 Reynolds Transport Theoreom Chapter 3
  12. 9/27 Conservation Laws – Mass Chapter 4
  13. 10/2 Conservation Laws – Momentum Chapter 4
  14. 10/4 Mid-Term Exam 1
  15. 10/9 Conservation Laws – Angular Momentum  
  16. 10/11 Navier-Stokes Equation Chapter 4
  17. 10/16 Rotating Frame of Reference Chapter 4
  18. 10/18 Energy Conservation Equations Chapter 4
  19. 10/23 Special Forms of Equations Chapter 4
  20. 10/25 Boussinesq Approximation Chapter 4
  21. 10/30 Vorticity Dynamics Chapter 5
  22. 11/1 Kelvin and Helmholtz Theorems Chapter 5
  23. 11/6 Vorticity Equation Chapter 5
  24. 11/8 Point Vortices Chapter 5
  25. 11/13 Scaling the Equations of Motion Chapter 13
  26. 11/15 Mid-Term Exam 2
    Thanksgiving Break
  27. 11/27 Geostrophic Balance Chapter 13
  28. 11/29 Dimensional Analysis Chapter 1
  29. 12/4 Rossby Waves Chapter 13
  30. 12/6 Internal Gravity Waves Chapter 8, 13 

Note on 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. 

Academic integrity statement

This course follows the Penn State defines academic integrity as "the pursuit of scholarly activity in an open, honest and responsible manner." Academic integrity includes "a commitment not to engage in or tolerate acts of falsification, misrepresentation, or deception." In particular, the University defines plagiarism as "the fabrication of information and citations; submitting other's work from professional journals, books, articles, and papers; submission of other student's papers, lab results or project reports and representing the work as one's own." Penalties for violations of academic integrity may include course failure. 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.

For example, uploading completed labs, homework, or other assignments to any study site constitutes a violation of this policy.

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 Student Disability Resources (SDR) website provides contact information for every Penn State campus: ( For further information, please visit the Student Disability Resources 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: 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 the Assistant Vice President for Student Affairs (AVPSA) and Student Care and Advocacy 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.

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Counseling and Psychological Services

Many students at Penn State face personal challenges or have psychological needs that may interfere with their academic progress, social development, or emotional wellbeing.  The university offers a variety of confidential services to help you through difficult times, including individual and group counseling, crisis intervention, consultations, online chats, and mental health screenings.  These services are provided by staff who welcome all students and embrace a philosophy respectful of clients’ cultural and religious backgrounds, and sensitive to differences in race, ability, gender identity and sexual orientation.  Services include the following:

Counseling and Psychological Services at University Park  (CAPS): 814-863-0395 Counseling and Psychological Services at Commonwealth Campuses Penn State Crisis Line (24 hours/7 days/week): 877-229-6400 Crisis Text Line (24 hours/7 days/week): Text LIONS to 741741

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 (see to your preferred e-mail account, so you don't miss any important information.