# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 221A: Mathematical Fluid Dynamics

Approved: 2009-03-01, Albert Fannjiang
Units/Lecture:
Fall, alternate years; 4 units; lecture/term paper or discussion
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
I.M. Cohen and P. K. Kundu, "Fluid Mechanics," Chapters 1, 3-7, (\$90)
Search by ISBN on Amazon: 0123737354
Prerequisites:
MAT 118B or consent of instructor
Course Description:
Kinematics and dynamics of fluids. The Euler and Navier-Stokes equations. Vorticity dynamics. Irrotational flow. Low Reynolds number flows and the Stokes equations. High Reynolds number flows and boundary layers. Compressible fluids. Shock waves.
Suggested Schedule:
1 Chapter 1 Introduction
1 3.1 - 3.3 Lagrangian and Eulerian descriptions
1 3.4 - 3.5 Streamline, path line, streak line
1 3.6 - 3.7 Strain rate
1 3.8 - 3.9 Vorticity, circulation, principal axes
1 Chapter 3.10 - 3.13 Shear flows, vortex flows, streamfunction
2 4.1 - 4.9 Conservation laws
1 4.10 - 4.11 Constitutive equation, Navier-Stokes equation
1 Chapter 4.13 Mechanical energy equation
1 4.14 - 4.15 Thermodynamics
1 4.16 - 4.17 Bernoulli equation
1 4.18 - 4.19 Boussinesq approximation, boundary conditions
1 5.1 - 5.3 Vortex lines, vortex tubes
2 5.4 Kelvin's Circulation Theorem, Helmholtz Vortex Theorems
1 5.5 Vorticity equation
1 5.6 Biot-Savart law
1 5.8 - 5.9 Vortex sheet
1 6.1 - 6.7 Irrotational flows
2 6.8 - 6.11 Flows and drags past 2-d body, Blasius Theorem, Kutta-Zhukhovsky Lift Theorem
1 6.20 - 6.22 Flows and drags around a 3-d body, d'Alembert paradox
1 7.1 - 7.5 Surface gravity waves
1 7.6 Deep and shallow water approximations
2 7.8 - 7.10 Group velocity, energy flux, wave dispersion
1 7.13 The Stokes wave
2 7.15 - 7.17 Internal waves