Fall 2017 

Instructor: Prof. Fuqing Zhang, 627A Walker,

Teaching Assistant: Dr. Y. Qiang Sun, 624 Walker,

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

Office hour: Monday 8:30-9:30 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. Plagiarism will not be tolerated. Late homework will be penalized 20% each day after the due date; it will not be accepted after the 5th day past due. 

Grading: Homework (20%), two in-class exams (25% each), and a final exam (30%). 

TextbookFluid Mechanics by Kundu, Cohen, and Dowling.  (Any edition of this book series is acceptable. PSU library has online version of 4th edition which will be primarily used for homework assignments).             

Course Outline

  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  

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.

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:

Reporting Bias-Motivated Incidents

Penn State takes great pride to foster a diverse and inclusive environment for students, faculty, and staff.  Acts of intolerance, discrimination, or harassment due to age, ancestry, color, disability, gender, gender identity, national origin, race, religious belief, sexual orientation, or veteran status are not tolerated ( and can be reported through Educational Equity via the Report Bias webpage.

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