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AMATH4180: Introduction to Fluid Dynamics

COURSE OUTLINE

  • Governing equations of fluid motion (ch 3-4)
      • A brief introduction to continuum hypothesis, Lagrangian and Eulerian description, rotating and non-rotating frame of reference, kinematics, stress and other forces, conservation of mass and momentum.
  • Vortex motion, irrotational flow, and water wave (ch 5-7)
      • Students will learn briefly fundamental laws of vortex motion - such as - circulation, vortex lines/tubes, vortex rings, vortex filaments, vortex instability, effects of viscosity, decay of trailing vortices, velocity potential, irrotational votex, sources/sinks, doublet, flow past a solid body, water wave etc.
  • Laminar boundary layer flow (ch 8-10)
      • We will discuss flow past solid obstacles, lift/drag on airfoils, boundary layer theory, perturbation techniques etc.
  • Introduction to turbulence and geophysical fluid dynamics (ch 11, 13-14)
      • A brief introduction to geophysical fluid dynamics and turbulence will present the gateway to the rich world of turbulence, introducing many open questions and unsolved puzzles. Students will be introduced the direct numerical simulation (DNS) method - for example - challenges of DNS, how intermittency affects DNS etc.

    Text book

    Most students may find lecture notes are sufficient. However, I strongly recommend to use at least one of the following text books. In the above outline, chapters are mentioned from Kundu and Cohen, but the course will not cover details of each chapters.
  • Main text book: Fluid Mechanics (5th Ed.) by Pijush K. Kundu and Ira M. Cohen(all lectures are prepared according to this text book).
  • Secondary text books are: Vortex dynamics by Saffman, P. G., Introduction to fluid dynamics by Batchelor, G. K., and Introduction to dynamic meteorlology by Holton, J. R.

    • Calendar description

    (Same as Physics 4205). Basic observations, mass conservation, vorticity, stress, hydrostatics, rate of strain, momentum conservation (Navier-Stokes equation), simple viscous and inviscid flows, Reynolds number, boundary layers, Bernoulli's and Kelvin's theorems, potential flows, water waves, thermodynamics.

    Prerequisite

    Physics 3220 and either AM4160 or Physics 3821.

    Note: Please talk to your Professor if you do not meet the prerequisite. You may be able to take the course if you have taken m3202, m3260, p2820.

    TEXT BOOK