School-wide Modular Program on Fluid Mechanics


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Sample physical origins of wave motion:

1. Taut string, elastic rod,

2. shallow seas, sound in a pipe,

3. traffic flow. Blood flow in arteries.

Visit to NDE laboratory of Prof. Wooh

Basic notions of waves:

4. Phase, phase velocity, frequency, wavenumber, etc.

One dimensional propagation:

5. Sinusoidal waves. Elastic strings,

6. Transient responses, Characteristics.

7. Dispersion. String in an elastic surrounding. Group velocity and energy transport.

8. Dispersion of transient waves, Method of stationary phase.

9. Scattering and radiation of harmonic waves. Radiation condition. Green's function.

Two dimensional propagation in infinite space:

10. Plane waves: Sound in homogeneous fluids.

11. Elastic solids: P and SV, SH waves.

12. Rayleigh waves in a half space.

13. Love waves in a layered medium.

14. Reflection and refraction of sinusoidal sound from a plane interface.

15. Reflection of a plane pulse.

16. Mode conversion of elastic waves.

17. Radiation of waves from point sources. Green functions in 2- and 3-D.

Waves in the sea:

18. Linearized equations.

19. Dispersion, scattering of sinusoidal waves by a cylinder.

20. Transients due to impulsive forcing.

21. Waves in a current, Ship waves.

22. Internal waves in a stratified fluid. Dispersion relation.

23. Internal waves in a flow. Lee waves behind an obstacle.

Depending on class interest and time we may discuss:

Waves through laminated media:

24. Effective equation for thin laminates.

25. Effective equation for thick laminates.


Nonlinear waves:

24. Traffic waves. Green and red lights.

25. Shocks and traffic jam.

26. Bores and hydraulic jumps.

27. Bore from the breaking of a dam.


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