\( \DeclareMathOperator{\tr}{tr} \newcommand\D{\mathrm{d}} \newcommand\E{\mathrm{e}} \newcommand\I{\mathrm{i}} \newcommand\bigOh{\mathcal{O}} \newcommand{\cat}[1]{\mathbf{#1}} \newcommand\curl{\vec{\nabla}\times} \newcommand{\CC}{\mathbb{C}} \newcommand{\NN}{\mathbb{N}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\RR}{\mathbb{R}} \newcommand{\ZZ}{\mathbb{Z}} % For +---- metric \newcommand{\BDpos}{} \newcommand{\BDneg}{-} \newcommand{\BDposs}{\phantom{-}} \newcommand{\BDnegg}{-} \newcommand{\BDplus}{+} \newcommand{\BDminus}{-} % For -+++ metric \newcommand{\BDpos}{-} \newcommand{\BDposs}{-} \newcommand{\BDneg}{} \newcommand{\BDnegg}{\phantom{-}} \newcommand{\BDplus}{-} \newcommand{\BDminus}{+} \)
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Topics - Fluid Mechanics

Flows and Solutions

As usual in the sciences, examples are more important than principles. There was a book by van Dyke, An Album of Fluid Motion. It would be nice to turn that into a bunch of GIFs or Javascript widgets, where the user could change the value of Reynolds numbers and other physical parameters. (Curiously, it appears the Lattice Boltzmann method is the preferred numerical method de jour.)

  • Hele-Shaw flow in 3-dimensions with "infinitesimally thin" fluids bounded between two sheets or surfaces. We can study Hele-Shaw flows past cylinders, airfoils, etc.
    • Lamb, Hydrodynamics, §71
    • L. M. Milne-Thomson, Theoretical Hydrodynamics §21.40
  • Rankine bodies and half-bodies

Things to ponder

  • Is there some well-defined form of turbulence? See mathoverflow.

Last Updated: Mon, 24 Apr 2023 09:16:49 -0700