This class introduces fluid dynamics to first year graduate students. The aim is to help students acquire an understanding of some of the basic concepts of fluid dynamics that will be needed as a foundation for advanced courses in atmospheric science, physical oceanography, ocean engineering, etc. The emphasis will be on fluid fundamentals, but with an atmosphere/ocean twist.
Expectations
It is presumed that students will have had a course in classical mechanics and differential equations, but no previous fluid dynamics experience (students who suspect that they may be significantly over or under qualified should contact the instructor).
A basic understanding of vector and tensor notation and algebra is assumed, as is a basic understanding of wave kinematics (dispersion relations, group velocity, phase velocity, etc.). Specific applications of each will be covered in the course, but little introductory material will be given. Brief refresher lectures will be given outside of scheduled class time. It is also assumed that students will have a working knowledge of Matlab®. If a student is lacking in any of these areas, they will be expected to bring themselves up to speed (students should feel free to contact the instructor for guidance).
Course Components
The course has four main components: 1) lectures, 2) reading assignments, 3) problem sets, and 4) short quizzes.
Lectures
The lectures are intended to introduce key concepts and to set them into the context of geophysical problems when appropriate. The lectures by themselves will not constitute an adequate introduction to fluid dynamics, and must be supplemented by reading assignments. Lectures will periodically be supplemented by short films.
Reading
The primary textbooks will be Fluid Mechanics by P. Kundu and I. Cohen (2004) (hereafter KC04) and Introduction to Geophysical FluidDynamics by B. CushmanRoisin (1994) (hereafter CR94). Both are strongly recommended for purchase. Three other useful texts are AtmosphereOcean Dynamics by A. E. Gill (1982) (hereafter G82), Physical Fluid Dynamics by D. J. Tritton (1988) (hereafter T88), and An Introduction to Dynamic Meteorology by J. R. Holton (1992) (hereafter H92). Another useful reference is the Online Publication: Price, James F. Topics in Fluid Dynamics: Dimensional Analysis, the Coriolis Force, and Lagrangian and Eulerian Representations. From time to time handouts from other sources will be provided in class or on the web. A basic guide to reading assignments is given in the readings section. More detailed reading assignments will be provided during class.
Problem Sets
Problem sets will be assigned most weeks and will contribute significantly towards final grades. Homework assignments will be made during lectures and will be listed on the course web site. In general, late homework will not be accepted, although exceptions for extreme situations will be considered on a casebycase basis.
Quizzes
Very short quizzes will be given approximately once a week and will cover material not yet addressed in class. These quizzes will be based on reading assignments that will be given in class and are designed to motivate students to properly prepare for lectures. They will be given at the beginning of class and consist of a few true/false questions and one or two questions that require short calculations or written explanations. Answers to the quiz questions will be sought interactively from the students immediately upon completion of the quiz. The questions will provide a roadmap to the day’s lecture and will hopefully facilitate interaction amongst the students and between the students and the instructor.
Exams and Grading
There will be a midterm examination, and there will be a final examination to be scheduled during the final exam period. Grading will be apportioned roughly 40% exam(s) and 60% problem sets. Quizzes will only be used for grading if a student is on the boundary between grades, or if a student systematically ignores or performs poorly on the quizzes.
References
Reading assignments will be made from KC04 and CR94. You should have a personal copy of KC04, and if you have the funds, a personal copy of CR94. Three additional books I find particularly useful are G82, T88, and H92. All books are on hold at the Lindgren Library and in the Physical Oceanography reading room.
Kundu, P. K., and I. M. Cohen. Fluid Mechanics. 3rd ed. New York: Elsevier Academic Press, 2004. ISBN: 0121782530.
CushmanRoisin, B. Introduction to Geophysical Fluid Dynamics. New York: Prentice Hall, 1994. ISBN: 0133533018.
Gill, A. E. AtmosphereOcean Dynamics. San Diego: Academic Press, 1982. ISBN: 0122835220.
Tritton, D. J. Physical Fluid Dynamics. Oxford: Oxford Science Publications, 1988. ISBN: 0198544936.
Holton, J. R. An Introduction to Dynamic Meteorology. San Diego: Academic Press, 1992. ISBN: 012354355X.
Online Publication: Price, James F. Topics in Fluid Dynamics: Dimensional Analysis, the Coriolis Force, and Lagrangian and Eulerian Representations.
Calendar
1 
Introduction
Class Aims
Class Administration (Problem Sets, Exams, Grades, etc.)
Scheduling Issues
Introduction to Fluid Dynamics 
Problem set 1 out 
25 
Kinematics of Fluid Flow
Eulerian and Lagrangian Representations of Flow
The Material Derivative
Trajectories, Streaklines, and Streamlines
CauchyStokes Theorem
The Velocity Gradient Tensor 
Problem set 1 due (Ses 2)
Problem set out (Ses 2)
Quiz 1 out (Ses 2)
Quiz 1 due (Ses 3)
Quiz 2 out (Ses 3)
Quiz 2 due (Ses 4)
Problem set 2 due (Ses 4)
Problem set 3 out (Ses 4)
Quiz 3 out (Ses 5) 
69 
Conservation Equations
Reynolds Transport Theorem
Momentum Equations (NavierStokes, Boussinesq form of NavierStokes, Euler)
Total Energy Equation, Mechanical Energy Equation, Heat Equation
2nd Law of Thermodynamics 
Quiz 3 due (Ses 6)
Problem set 3 due (Ses 7)
Problem set 4 out (Ses 7)
Problem set 4 due (Ses 9) 
1013 
Vortex Flows, Circulation, and Vorticity
Bernoulli Functions
Solid Body Rotation, Point Vortex, Rankine Vortex
Stokes' Theorem
Potential Flows: Interacting Point Vortices
Kelvin's Circulation Theorem
Helmholtz Vortex Theorems
Vorticity Equation 
Problem set 5 out (Ses 10)
Quiz 4 out (Ses 10)
Quiz 4 due (Ses 11)
Problem set 5 due (Ses 12)
Problem set 6 out (Ses 12)
Quiz 5 out (Ses 12)
Quiz 5 due (Ses 13) 
1415 
Impact of The Earth’s Rotation
Momentum Equations in a Rotating Frame
Centripetal Acceleration, Coriolis Acceleration
Vorticity Equation in a Rotating Frame
Kelvin's Circulation Theorem in a Rotating Frame 
Quiz 6 out (Ses 14)
Problem set 6 due (Ses 15)
Problem set 7 out (Ses 15)
Quiz 6 due (Ses 15) 
1618 
GFD Kinematics
Simplified Momentum Equations
Inertial Flow, Geostrophy, Gradient Wind, Cyclostrophic Flow, Isallobaric Flow
Impact of Viscosity
TaylorProudman Theorem
Thermal Wind 
Quiz 7 out (Ses 16)
Quiz 7 due (Ses 17)
Problem set 7 due (Ses 17)
Problem set 8 out (Ses 17) 
1920 
Ekman Layers
Brief Boundary Layer Introduction
Mass Transport in Ekman Layer; Ekman Pumping and Suction
Ekman Spiral
Sverdrup Transport 
Problem set 8 due (Ses 19)
Problem set 9 out (Ses 20) 
2124 
Waves
Beta Effect
Wave Kinematics
Barotropic, Fixed Depth Rossby Waves
Shallow Water Equations, Shallow Water Gravity Waves, InertiaGravity Waves, Kelvin Waves
Potential Vorticity
Barotropic, QuasiGeostrophic Rossby Waves
KelvinHelmholz Instability 
Problem set 9 due (Ses 21) 
25 

Final exam due 