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#### Course Highlights

#### Course Description

#### Technical Requirements

MATLAB® software is required to run the .m files found on this course site. File decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site.

# Syllabus

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. Cushman-Roisin (1994) (hereafter CR94). Both are strongly recommended for purchase. Three other useful texts are *Atmosphere-Ocean 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 case-by-case 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 mid-term 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.

Cushman-Roisin, B. *Introduction to Geophysical Fluid Dynamics*. New York: Prentice Hall, 1994. ISBN: 0133533018.

Gill, A. E. *Atmosphere-Ocean 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

LEC # | TOPICS | KEY DATES |
---|---|---|

1 | IntroductionClass Aims Class Administration (Problem Sets, Exams, Grades, etc.) Scheduling Issues Introduction to Fluid Dynamics |
Problem set 1 out |

2-5 | Kinematics of Fluid FlowEulerian and Lagrangian Representations of Flow The Material Derivative Trajectories, Streaklines, and Streamlines Cauchy-Stokes 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) |

6-9 | Conservation Equations Reynolds Transport Theorem Momentum Equations (Navier-Stokes, Boussinesq form of Navier-Stokes, 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) |

10-13 | Vortex Flows, Circulation, and VorticityBernoulli FunctionsSolid 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) |

14-15 | Impact of The Earth’s RotationMomentum Equations in a Rotating FrameCentripetal 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) |

16-18 | GFD KinematicsSimplified Momentum EquationsInertial Flow, Geostrophy, Gradient Wind, Cyclostrophic Flow, Isallobaric Flow Impact of Viscosity Taylor-Proudman 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) |

19-20 | Ekman LayersBrief Boundary Layer IntroductionMass Transport in Ekman Layer; Ekman Pumping and Suction Ekman Spiral Sverdrup Transport |
Problem set 8 due (Ses 19) Problem set 9 out (Ses 20) |

21-24 | WavesBeta EffectWave Kinematics Barotropic, Fixed Depth Rossby Waves Shallow Water Equations, Shallow Water Gravity Waves, Inertia-Gravity Waves, Kelvin Waves Potential Vorticity Barotropic, Quasi-Geostrophic Rossby Waves Kelvin-Helmholz Instability |
Problem set 9 due (Ses 21) |

25 | Final exam due |