Office hour Wednesday 11-11:50pm.

Pre-requisites: Vector analysis, differential equations, mechanics

Texts

• I.M Cohen and P.K. Kundu: Fluid Mechanics, Third Edition, 2004,
• (Supplement) L. D. Landau and E. M. Lifshitz: Fluid Mechanics, Second Edition, 1987

Topics

• Dimensional and scaling analysis
• Laminar flows: Pipe flows, channel flows, wakes, jets.
• Boundary layers
• Instability
• Turbulence
• Microfluids

Gallery

• Flows around a sphere at various Reynolds number
• Hele-Shaw flow around a circular obstable.
• (Movie) Simulated flow past a cylinder at Reynolds number 100,000
  Compared with Real flow at the same Reynolds number
• Von Karman vortex
  • Numerically simulated Karman vortex street
  • Simulated streamlines of Karman vortex street
  • Von Karman vortex street off the Chilean coast near the Juan Fernandez Islands
  • Looking down von Karman vortex street in clouds over Alaska islands
• Wave cloud formation due to Kelvin-Helmholtz instability
• Instability in axi-symmetric jet
• Turbulent boundary layer
• Pressure and velocity vectors in the plane perpendicular to a numerically simulated pipe flow (red, low pressure region; blue, high pressure region; mesh spacings, 50 wall units)
• Flow visualization techniques
• Cloud formation is the Nature's visualization tool!
• Methods for visualizing microflows
• Coriolis force in action:
  • Hurricanes (in the northern hemisphere) rotate counterclockwise.
    • Hurricane Floyd in the Atlantic
    • Typhoons in the N.W. Pacific
    
    
  • Cyclones (in the southern hemisphere) rotate clockwise.
    • Southern Pacific cyclones .
• Water waves:
  • Particle trajectories in water waves
  • Stokes wave: nonlinear periodic wavetrains
  • Wave breaking
• John Scott Russell and the solitary wave
• Solitary wave in Russell's water tank

Interesting articles

• L. N. Trefethen, A.E. Trefethen, S.C. Reddy and T.A. Driscoll, Hydrodynamic stability without eigenvalues. Science 261, 578-584 (1993).
• S. C. Reddy; P. J. Schmid; D. S. Henningson, Pseudospectra of the Orr-Sommerfeld Operator SIAM J Applied Mathematics, Vol. 53, No. 1. (Feb., 1993), pp. 15-47.
• Marten T. Landahl, Wave Breakdown and Turbulence. SIAM Journal on Applied Mathematics, Vol. 28, No. 4. (Jun., 1975), pp. 735-756.
• E.N. Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141 (1963).
• D. J. Benney and S.A. Maslowe, The evolution in space and time of nonlinear waves in parallel shear flows. Studies in Applied Mathematics 54, 181-205 (1975).

Assignments

• 1st assignment: 1,2 plus one assigned in class (Chapter 8) Solution 1
• 2nd assignment: 1,2,3,4, 6 (Chapter 9) plus: Determine the free surfaces given in Figure 9.7 and 9.8. Solution 2
• Solution 3
• Solution 4
• HW 5 Solution 5
• HW 6