Lecture notes: Advanced Fluid Mechanics

Advanced Fluid Mechanics

Miscellaneous rough lecture notes. All of this material is adapted from (and often expands on) other sources. In particular, several of these sets of notes are expanded versions of homework solutions and notes originally developed by Professor Stephen Morris at the University of California at Berkeley. The other major source is Drazin & Reid’s Hydrodynamic Stability. The plasma material is an amalgam from several sources, including Hughes’ MHD book.

I) Plasma Physics Primer Part I (many typos)

II) Plasma Physics Primer Part II (many typos)

III) Spin-Up of a Fluid in a Rotating Cylinder (complicated/interesting example of asymptotic analysis)

IV) Nonlinear Capillary Instability Pt. I (short overview of nonlinear dynamics/bifurcation theory)

V) Nonlinear Capillary Instability Pt. II (continues Part I – fluid collars & lenses)

VI) Asymptotic Analysis of Early Time Flow around an Impulsively Started Cylinder (interesting asymptotic analysis of unsteady coupled potential and boundary layer flows)

VII) Rayleigh-Benard Stability Problem (classic thermal stability problem)

VIII) Capillary Instability of a Thin Annular Film (linear stability analysis of film break-up into collars and lenses)

IX) Linear and Nonlinear Hydrodynamic Stability (primer/overview)

X) Capillary Instability of a Jet (example linear stability problem)

XI) Green’s Function in Low Reynolds Number Flow (short overview)

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