Graduate fluid mechanics course on classical and modern approaches to hydrodynamics. Topics cover three areas, (1) surface waves, (2) flow instability, and (3) vortex dynamics. Wave topics include linear dispersive and nondispersive waves, weakly nonlinear waves, and viscous effects, with special attention to surface tension phenomena. Flow instabilities include gravitational, capillary, thermal, centrifugal, and viscous instabilities. Topics in vortex dynamics include vortex laws and flow invariants, generation and decay of vorticity, and vortex-boundary interaction.
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